Guia_4.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Guia 4.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "XA712-qQ9TP9"
      ],
      "authorship_tag": "ABX9TyMM8XN8X67CJk8JpQA/EN9f",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AnaGutson/AlgebraII/blob/main/Guia_4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Guía 4**"
      ],
      "metadata": {
        "id": "NceeY2MU0k7V"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RMrGYW2S0YSI"
      },
      "outputs": [],
      "source": [
        "from sympy import *\n",
        "from sympy import I as i\n",
        "init_printing(use_unicode=True)\n",
        "from typing import List, Dict\n",
        "import numpy as np\n",
        "from numpy import linspace\n",
        "import matplotlib.pyplot as plt\n",
        "from math import e as e"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **General**"
      ],
      "metadata": {
        "id": "kGBSomiI8GcR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Triángulo de Pascal**"
      ],
      "metadata": {
        "id": "T6e9_42mC2iQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "DvRkPDP9N_A6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "1C84ZyoBODLL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Producto Vectorial**"
      ],
      "metadata": {
        "id": "g8rw1LwY8IpB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def producto_vectorial(A,B):\n",
        "  a = Matrix([[A[1], A[2]], [B[1], B[2]]]).det()\n",
        "  b = Matrix([[A[0], A[2]], [B[0], B[2]]]).det()\n",
        "  c = Matrix([[A[0], A[1]], [B[0], B[1]]]).det()\n",
        "  return Matrix([a, -b, c])"
      ],
      "metadata": {
        "id": "oMx8awBI8ONr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Traza**"
      ],
      "metadata": {
        "id": "v4rD3fCktBiu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "9x4gdC4VtG0-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Matrices**"
      ],
      "metadata": {
        "id": "6wCzuFol7Q9J"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "  A.inv                                   -> La inversa de A\n",
        "  A.T                                     -> La transpuesta de A\n",
        "  A.transpose()                           -> La transpuesta de A\n",
        "  A.det                                   -> Determinante de A\n",
        "  A.trace()                               -> Traza de A\n",
        "  A.normalized()                          -> Matriz normalizada\n",
        "  A.rref()                                -> Matriz triangulada\n",
        "  A[1,0]                                  -> Posicion segunda fila primera columna\n",
        "  A[:,0]                                  -> La primera columna de A\n",
        "  A[0,:]                                  -> La primera fila de A\n",
        "  A.col(0)                                -> La primera columna de A\n",
        "  A.subs(t, pi/3)                         -> Reemplaza las t por pi/3\n",
        "  A.subs({x1:1, x2:5, x3:7})              -> Reemplaza x1 por 1, x2 por 5...\n",
        "  Z = zeros(2,1)                          -> Matriz de 0s de 2 filas 1 columna\n",
        "  unos = ones(2,1)                        -> Matriz de 1s de 2 filas 1 columna\n",
        "  eye(n)                                  -> Matriz identidad en n x n\n",
        "  Matrix.hstack(v1,v2)                    -> Matriz con columnas v1, v2\n",
        "  Matrix.vstack(v1,v2)                    -> Matriz con filas v1, v2\n",
        "  Lambda = diag(2, 2, 3)                  -> Matriz diagonal\n",
        "  x, parametro = B.gauss_jordan_solve(v)  -> Solucion de B.x = v\n",
        "  simplify(A)                             -> Simplifica A\n",
        "  expand(A)                               -> Expande A\n",
        "  n, m = A.shape                          -> Cantidad filas y columnas de A\n",
        "'''\n",
        "\n",
        "\n",
        "#Escritura de matriz, ejemplos:\n",
        "\n",
        "U = Rational('1/3') * Matrix([[ 2, 2, 1],\n",
        "                              [-2, 1, 2],\n",
        "                              [ 1,-2, 2]])\n",
        "\n",
        "#___________________________________________\n",
        "\n",
        "t = Symbol('t')\n",
        "A = Matrix([[ cos(t), -sin(t)],\n",
        "            [ sin(t), cos(t)]])\n",
        "A.subs(t, pi/3)\n",
        "\n",
        "\n",
        "def matriz_con_elementos_potenciados(A, pot):\n",
        "  m, n = A.shape\n",
        "  M = Matrix()\n",
        "  for i in range(m):\n",
        "    M_a_agregar = Matrix([A[i,0]**pot]) \n",
        "    M = M.vstack(M, M_a_agregar)\n",
        "  return M\n",
        "\n",
        "def rango(A):\n",
        "  return len(A.columnspace())\n"
      ],
      "metadata": {
        "id": "tRH_o0pn7P4J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Polinomios**"
      ],
      "metadata": {
        "id": "4n8w6ECPNN1k"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "  diff(p,x) -> La derivada de p respecto de x\n",
        "  p.subs(x,1) -> p(1)\n",
        "  p.factor() -> factoriza un polinomio\n",
        "  p.roots() -> las raices del polinomio\n",
        "  solve(p) -> las raices del polinomio\n",
        "  P = plot(p,(x,0,2)) -> grafico del polinomio con x entre 0 y 2\n",
        "  P = plot(*L, (x,0,2)) -> grafico de una lista de polinomios con x entre 0 y 2\n",
        "  P[0].line_color = 'red' -> color del primer polimonio\n",
        "  P.show() -> muestra el grafico del polinomio con x entre 0 y 10\n",
        "'''\n",
        "\n",
        "#Escritura de polimomio, ejemplos:\n",
        "\n",
        "x, a0, a1, a2 = symbols('x, a0, a1, a2')\n",
        "p = a0 + a1*x + a2*x**2"
      ],
      "metadata": {
        "id": "UBbd4bBqNUvk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Combinación Lineal**"
      ],
      "metadata": {
        "id": "4IwtbBsS_75d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gauss_jordan_con_generadores(A: Matrix, z: Matrix): #devuelve la solucion de gauss jordan entera, la sol part y sus generadores\n",
        "  x, p = A.gauss_jordan_solve(z) \n",
        "  \n",
        "  #hallo sol particular\n",
        "  x_0 = x\n",
        "  for i in range(len(p)):  \n",
        "    x_0 = x_0.subs({p[i]:0}) \n",
        "  \n",
        "  #hallo generadores\n",
        "  generadores = []\n",
        "  for i in range(len(p)):\n",
        "    x_i = x - x_0\n",
        "    for j in range(len(p)):\n",
        "      if j != i:\n",
        "        x_i = x_i.subs({p[j]:0})\n",
        "    x_i = x_i.subs({p[i]:1})\n",
        "    generadores.append(x_i)\n",
        "    \n",
        "  return x, x_0, generadores"
      ],
      "metadata": {
        "id": "mFvuloKi-8zs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Independencia Lineal**"
      ],
      "metadata": {
        "id": "5DGVva2AKLtV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def encontrar_vector_li_a_conjunto(A: List[Matrix]):  #Principio de sustitución de Steinez\n",
        "  cant_filas, _ = A[0].shape\n",
        "  A_ld = Matrix.hstack(*A, eye(cant_filas,cant_filas))\n",
        "  A_li = obtener_vectores_li(A_ld)\n",
        "  return A_li\n",
        "\n",
        "#_______________________\n",
        "\n",
        "def obtener_vectores_li(A: Matrix):\n",
        "  E_A, pivotes_A = A.rref()\n",
        "  A_li = []\n",
        "  for pivote in pivotes_A:\n",
        "      A_li.append(A.col(pivote))        #De la matriz original\n",
        "  return A_li\n",
        "\n",
        "#_______________________\n",
        "\n",
        "'''\n",
        "  Ejemplo:\n",
        "  B = [Matrix([a, 1, 2]), Matrix([3, 2, 3]), Matrix([1, -a, 1])] #una lista\n",
        "  encontrar_a(B, a)\n",
        "'''\n",
        "a = Symbol('a')\n",
        "def encontrar_a(B: List[Matrix], a: Symbol): #Halla el o los valores que puede tener a para que los vectores sean linealmente independientes: formen una base\n",
        "\n",
        "    return solve(det(Matrix.hstack(*B)), a)"
      ],
      "metadata": {
        "id": "FFwB62zfy_Cx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Ínfimo y Supremo**"
      ],
      "metadata": {
        "id": "fWz2KnECXIyQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "cant_neg: cantidad de vectores que pertenecen al segundo subespacio\n",
        "'''\n",
        "def interseccion_S1_S2_dos_lados(S1: List[Matrix], S2: List[Matrix]):\n",
        "  S2_neg = [i*(-1) for i in S2]\n",
        "  B_S1_S2 = Matrix.hstack(*S1,*S2_neg)\n",
        "  cant_S2 = len(S2)\n",
        "  nul_B_S1_S2 = B_S1_S2.nullspace()\n",
        "  S1_int_S2 = []\n",
        "  for v in nul_B_S1_S2:\n",
        "      v[(-1)*cant_S2:,:] = zeros(cant_S2, 1)\n",
        "      S1_int_S2.append(B_S1_S2 * v)\n",
        "\n",
        "  return S1_int_S2\n",
        "\n",
        "def union_S1_S2(S1: List[Matrix], S2: List[Matrix]):\n",
        "    B_S1_S2 = Matrix.hstack(*S1,*S2)\n",
        "    S1_un_S2 = obtener_vectores_li(B_S1_S2)\n",
        "    return S1_un_S2                "
      ],
      "metadata": {
        "id": "FaKOnSErXQ-N"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Transformaciones Lineales**"
      ],
      "metadata": {
        "id": "3JjXGSiimXkF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Parametros: T una t.l, B una base    \n",
        "#Devuelve la matriz de la transformacion lineal T a partir de T y una base\n",
        "def matriz_tl_con_tl_y_base(T: Matrix, B: List[Matrix]): #la matriz de T a partir de B\n",
        "  TB = Matrix() \n",
        "  for i in B:\n",
        "    ti = T*i\n",
        "    TB = Matrix.hstack(TB, ti)\n",
        "  return TB\n",
        "\n",
        "\n",
        "#Parametros: B una base, W  los transformados de B    \n",
        "#Devuelve la matriz de la transformacion lineal T a partir de una base, y los transformados de la base    \n",
        "def matriz_tl_con_base_y_transformados(B: List[Matrix], W: List[Matrix]): #la matriz de T a partir de los transformados de B\n",
        "    return Matrix.hstack(*W) * Matrix.hstack(*B).inv()\n",
        "\n",
        "#Parametros: T una t.l, p una lista de polinomios\n",
        "#Devuelve T(polinomios)\n",
        "def transformacion_lineal_pol(T: Matrix, polinomios):\n",
        "  polinomios = [Matrix([i]) for i in polinomios]\n",
        "  P = Matrix.vstack(*polinomios)\n",
        "  return (expand(T*P))[0,0] #devuelvo el elemento que está en formato Matriz"
      ],
      "metadata": {
        "id": "5Oizq1X4pox_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Monomorfismo, epimorfismo e isomorfismo**"
      ],
      "metadata": {
        "id": "5EM9VJTHAiOX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def clasificacion(At: Matrix):\n",
        "  imT = At.columnspace()\n",
        "  nuT = At.nullspace()\n",
        "\n",
        "  dimW, dimV = At.shape\n",
        "  if len(nuT) == 0 and len(imT) == dimW:\n",
        "    return 'T es un isomorfismo'\n",
        "  else:\n",
        "    if len(nuT) == 0:\n",
        "      return 'T es un monomorfismo'\n",
        "    elif len(imT) == dimW:\n",
        "      return 'T es un epimorfismo'\n",
        "  \n",
        "  return 'T no es un monomorfismo ni un epimorfismo'"
      ],
      "metadata": {
        "id": "Hn4xmzjBMRwF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Imagen y Preimagen**"
      ],
      "metadata": {
        "id": "7Lf_UiFCisDN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''\n",
        "    Halla la imagen por T de un subespacio S dada una base B y la imagen por T de B\n",
        "    \n",
        "    B: es una lista de vectores que conforman la base B\n",
        "    W: es una lista de vectores que corresponden a las imágenes de los vectores de la base B\n",
        "    S: es una lista de vectores que generan el subespacio S\n",
        "'''\n",
        "def imagen_por_T_de_S_con_B_y_W(B: List[Matrix], W: List[Matrix], S: List[Matrix]): \n",
        "    # Obtengo la matriz de T\n",
        "    A_T = matriz_tl_con_base_y_transformados(B, W)\n",
        "\n",
        "    # Obtengo los transformados de S    \n",
        "    imagen_T_S = A_T * Matrix.hstack(*S)\n",
        "\n",
        "    # Armo una base con los transformados de S    \n",
        "    base_T_S = obtener_vectores_li(imagen_T_S)\n",
        "    \n",
        "    return base_T_S\n",
        "\n",
        "#_______________________________________________________________________________\n",
        "\n",
        "\n",
        "#Forma 1, explicada arriba\n",
        "def preimagen_subespacio_con_At(At: Matrix, Au: Matrix):\n",
        "  \n",
        "    return (Au*At).nullspace()\n",
        "    \n",
        "#_______________________________________________________________________________\n",
        "\n",
        "#Forma 2, explicada arriba\n",
        "def preimagen_subespacio_con_B_y_W(B: List[Matrix], W: List[Matrix], Au: Matrix):\n",
        "    B_matrix = Matrix.hstack(*B)\n",
        "    W_matrix = Matrix.hstack(*W)\n",
        "\n",
        "    sol = (Au * W_matrix).nullspace()\n",
        "    preimagen_U = B_matrix * Matrix.hstack(*sol)\n",
        "\n",
        "    #Obtengo una base de la preimagen\n",
        "    B_T_inv_U = obtener_vectores_li(preimagen_U)\n",
        "    \n",
        "    return B_T_inv_U    \n"
      ],
      "metadata": {
        "id": "sa3T4_b6kfhw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Coordenadas**"
      ],
      "metadata": {
        "id": "Z6GO_F44k4B_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def coordenadas_v_en_B(v: Matrix, B):\n",
        "  M_B = Matrix.hstack(*B) \n",
        "  \n",
        "  #v = M_B * [v]^B\n",
        "  vB, pivotes = M_B.gauss_jordan_solve(v)\n",
        "  \n",
        "  return vB\n",
        "\n",
        "def imagen_de_T_con_At_B_Bprima(At_B_Bprima: Matrix, Bprima: List[Matrix]):\n",
        "  \n",
        "  #Obtengo Col(At) = gen{[T(v)]^B' ... }\n",
        "  imagenBprima = At_B_Bprima.columnspace()\n",
        "\n",
        "  #Quiero Im(T) = gen{T(v) ... }\n",
        "  #Es decir, necesito escribir los [T(v)]^B' como T(v)\n",
        "  #T(v) = M_Bprima * [T(v)]^B'\n",
        "  imagen = Matrix.hstack(*Bprima) * Matrix.hstack(*imagenBprima)\n",
        "  \n",
        "  base_imagen = obtener_vectores_li(imagen)\n",
        "  \n",
        "  return base_imagen\n",
        "\n",
        "def nucleo_de_T_con_At_B_Bprima(At_B_Bprima: Matrix, B: List[Matrix]):\n",
        "  \n",
        "  #Obtengo Nul(At) = gen{[x]^B ... }\n",
        "  nucleoB = At_B_Bprima.nullspace()\n",
        "\n",
        "  #Quiero Nu(T) = gen{x ... }\n",
        "  #Es decir, necesito escribir los [x]^B como x\n",
        "  #x = M_B * [x]^B\n",
        "  nucleo = Matrix.hstack(*B) * Matrix.hstack(*nucleoB)\n",
        "  \n",
        "  base_nucleo = obtener_vectores_li(nucleo)\n",
        "  \n",
        "  return base_nucleo\n",
        "\n",
        "def nucleo_de_T_con_At_B_Bprima_pol(At_B_Bprima: Matrix, B: List[Matrix]):\n",
        "  \n",
        "  #Obtengo Nul(At) = gen{[x]^B ... }\n",
        "  nucleoT = T1oT2inv_Eprima_E.nullspace()\n",
        "  \n",
        "  #Quiero Nu(T) = gen{x ... }\n",
        "  #Es decir, necesito escribir los [x]^B como x\n",
        "  #x = M_B * [x]^B\n",
        "\n",
        "  nucleo = Ep * Matrix.hstack(*nucleoT)\n",
        "  \n",
        "  return nucleo "
      ],
      "metadata": {
        "id": "3Kq0Qdvf0amm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Graficar"
      ],
      "metadata": {
        "id": "58c2pW0WG7HE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_vector2d(*vectors,xlim=(0,1),ylim=(0,1)):\n",
        "  fig, ax = plt.subplots(1,1,figsize=(7,7))\n",
        "\n",
        "  for v in vectors:\n",
        "    x, y = float(v[0]), float(v[1])\n",
        "    ax.arrow(0,0,x,y,head_width=0.05, head_length=0.05, fc='k', ec='k')\n",
        "  \n",
        "  ax.set_xlim(*xlim)\n",
        "  ax.set_ylim(*ylim)\n",
        "  ax.grid(True)\n",
        "  ax.set_xlabel('$x_1$')\n",
        "  ax.set_ylabel('$x_2$')\n",
        "  fig.show()\n",
        "  return fig, ax\n",
        "\n",
        "def plot_recta_simetria(theta,ax):\n",
        "  x1, x2 = ax.get_xlim()\n",
        "\n",
        "  if theta not in [pi/2,-pi/2]:\n",
        "    y1 = float(tan(theta/2*x1))\n",
        "    y2 = float(tan(theta/2*x2))\n",
        "  else:\n",
        "    y1, y2 = ax.get_ylim()\n",
        "  \n",
        "  ax.arrow(x1,y1,x2-x1,y2-y1,fc='b',ec='b')\n",
        "  return ax\n",
        "\n",
        "def graficar_dos_funciones(f1,f2):\n",
        "  p1 = plot(f1,xlim=(-1,1),ylim=(-2,2),show=False,line_color='blue')\n",
        "  p2 = plot(f2,xlim=(-1,1),ylim=(-2,2),show=False,line_color='red')\n",
        "  p1.append(p2[0])\n",
        "  p1.show()\n",
        "\n",
        "v1, v2 = Matrix([1,0]), Matrix([0,1])\n",
        "fig, ax = plot_vector2d(v1,v2,xlim=(-2.1,2.1),ylim=(-2.1,2.1))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "3ABiN0AfG-Tq",
        "outputId": "11f652a3-40eb-46d9-e039-12f436a919a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Proyecciones y Simetrías**"
      ],
      "metadata": {
        "id": "-mFiNtAewIyZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def simetria(v,theta):\n",
        "  S = Matrix([[cos(theta), sin(theta)],\n",
        "              [sin(theta), -cos(theta)]])\n",
        "  w = S * v\n",
        "  return w\n",
        "\n",
        "v = Matrix([1,1])\n",
        "theta = pi/8\n",
        "\n",
        "v_s = simetria(v,theta)\n",
        "fig, ax = plot_vector2d(v,v_s,xlim=(-2,2),ylim=(-2,2))\n",
        "ax = plot_recta_simetria(theta,ax)\n",
        "\n",
        "#__________________________\n",
        "\n",
        "def tipo_tl(T: Matrix):\n",
        "  T2 = T*T\n",
        "  n,m = T2.shape\n",
        "  if T2 == T:\n",
        "    return 'Es una proyección'\n",
        "  elif T2 == eye(n,n):\n",
        "    return 'Es una simetría'\n",
        "  return 'No es proyección ni simetría'\n",
        "  \n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "xIEmwO4dI9To",
        "outputId": "3534712c-5df3-4b8d-c787-aa484a2f7a4b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Rotaciones**"
      ],
      "metadata": {
        "id": "HEDLs3WI4Xx0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def rotacion(v,theta):\n",
        "  R = Matrix([[cos(theta), -sin(theta)],\n",
        "              [sin(theta), cos(theta)]])\n",
        "  w = R * v\n",
        "  return w\n",
        "\n",
        "#Ejemplo\n",
        "v = Matrix([0,1])\n",
        "theta = pi/4\n",
        "\n",
        "v_r = rotacion(v,theta)\n",
        "fig, ax = plot_vector2d(v,v_r,xlim=(-2,2),ylim=(-2,2))"
      ],
      "metadata": {
        "id": "PenWO-UUHR97",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "outputId": "72d3dd6e-ccff-4321-a153-856546299199"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Ecuaciones Diferenciales**"
      ],
      "metadata": {
        "id": "rWyvd90Zr0TS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def nucleo_de_operador_diferencial(L):\n",
        "    x = Symbol('x')\n",
        "    Nu_L = set()\n",
        "    raices = str(L).split('*')\n",
        "    l = 1\n",
        "    for raiz in raices:\n",
        "\n",
        "      if '-' in raiz:\n",
        "        index = raiz.index('-') + 1\n",
        "        l = (int(raiz[index]))*(-1)\n",
        "      elif '+' in raiz:\n",
        "        index = raiz.index('+') + 1\n",
        "        l = (int(raiz[index]))\n",
        "      else:\n",
        "        display(raiz)\n",
        "      \n",
        "      if '^' in raiz:\n",
        "        k = int(raiz.split('^')[1])\n",
        "      else:\n",
        "        k = 1\n",
        "          \n",
        "      for i in range(k):\n",
        "        Nu_L.add((x**(i))*exp(-l*x))\n",
        "\n",
        "    return Nu_L\n",
        "\n",
        "def gen_solucion_particular(L, AoL):\n",
        "    Nu_L = nucleo_de_operador_diferencial(L)\n",
        "    Nu_AoL = nucleo_de_operador_diferencial(AoL)\n",
        "    Nu = set()\n",
        "    Nu = Nu_L | Nu_AoL\n",
        "    Nu = Nu - Nu_L\n",
        "    return list(Nu)\n",
        "\n",
        "D, I = symbols('D I')\n",
        "L = '(D-5I)*(D+2I)^2'\n",
        "AoL = '(D-5I)*(D+2I)^5'\n",
        "gen_solucion_particular(L, AoL)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "id": "m4ua9gvWgR5R",
        "outputId": "5fcc2e2d-eec4-4441-ad4c-962adfc8fde0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ x^{2} e^{- 2 x}, \\  x^{4} e^{- 2 x}, \\  x^{3} e^{- 2 x}\\right]$",
            "text/plain": [
              "⎡ 2  -2⋅x   4  -2⋅x   3  -2⋅x⎤\n",
              "⎣x ⋅ℯ    , x ⋅ℯ    , x ⋅ℯ    ⎦"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Producto Interno**"
      ],
      "metadata": {
        "id": "0gdoW37ECSui"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def producto_interno_canonico(x, y, G: Matrix = None):\n",
        "    return (y.T * x)[0]\n",
        "\n",
        "def producto_interno_por_definicion(x: Matrix, y: Matrix, G: Matrix):\n",
        "    return (y.T * G * x)[0]\n",
        "    \n",
        "def producto_interno_polinomios_integral(p, q, G:Matrix = None, limite_inferior=-1, limite_superior=1, a=1):\n",
        "    return integrate(p * q * a, (x, limite_inferior, limite_superior))\n",
        "\n",
        "def norma(x, producto_interno, G: Matrix=None):\n",
        "    return sqrt(producto_interno(x, x, G))\n",
        "\n",
        "#A.norm() -> la norma con el producto interno canónico, es decir, producto escalar"
      ],
      "metadata": {
        "id": "IzXcCwRlCICZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Matriz de Gram**"
      ],
      "metadata": {
        "id": "Ti_7qrZrk5r5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def matriz_gram(producto_interno, B):\n",
        "    n = len(B) # Cantidad de componentes de la base\n",
        "\n",
        "    # Inicializo la matriz de Gram\n",
        "    G = zeros(n,n)\n",
        "    \n",
        "    # Lleno la matriz calculando los productos internos\n",
        "    for i, p in enumerate(B):\n",
        "        for j, q in enumerate(B):\n",
        "            G[i,j] = producto_interno(p,q)\n",
        "    return G \n",
        "\n",
        "def matriz_gram_con_G(producto_interno, B, GB):\n",
        "    n = len(B) # Cantidad de componentes de la base\n",
        "\n",
        "    # Inicializo la matriz de Gram\n",
        "    G = zeros(n,n)\n",
        "    \n",
        "    # Lleno la matriz calculando los productos internos\n",
        "    for i, p in enumerate(B):\n",
        "        for j, q in enumerate(B):\n",
        "            G[i,j] = producto_interno(p,q, GB)\n",
        "    return G \n",
        "\n",
        "def area_de_un_paralelogramo(G: Matrix):\n",
        "    return sqrt(G.det())\n",
        "\n",
        "def area_de_un_triangulo(G: Matrix):\n",
        "    return area_de_un_paralelogramo(G)/2"
      ],
      "metadata": {
        "id": "v39Ij9o8CVIo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Proyección Ortogonal**"
      ],
      "metadata": {
        "id": "QGijsACADRMS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def y_tilda(y, B: List, producto_interno, G: Matrix = None):\n",
        "  return Matrix([producto_interno(y, B[i], G) for i in range(len(B))])\n",
        "\n",
        "def proyeccion_ortogonal_de_v_a_S_un_generador(v, gen, producto_interno, G: Matrix = None):\n",
        "  return producto_interno(v, gen, G) * gen / norma(gen, producto_interno, G)**2\n",
        "\n",
        "def proyeccion_ortogonal_de_v_a_S_varios_generadores(y, B, producto_interno):\n",
        "  G = matriz_gram(producto_interno, B)\n",
        "  y_tilda = y_tilda(y, B, producto_interno)\n",
        "  p_coord = G.T.inv() * y_tilda\n",
        "  p_hat = (Matrix.hstack(*B) * p_coord)\n",
        "  return p_hat\n",
        "  \n",
        "def proyeccion_ortogonal_de_v_a_S_varios_generadores_pol(y, B, producto_interno):\n",
        "  G = matriz_gram(producto_interno, B)\n",
        "  ytilda = y_tilda(y, B, producto_interno)\n",
        "  p_coord = G.T.inv() * ytilda\n",
        "  p_hat = (Matrix(B).T * p_coord)\n",
        "  return p_hat\n",
        "\n",
        "def proyeccion_ortogonal_de_v_a_S_ortogonal(v: Matrix, B: List[Matrix]):\n",
        "  m, n = v.shape\n",
        "  P_S_v = zeros(m, n)\n",
        "  for i in range(len(B)):\n",
        "    u = B[i]\n",
        "    P_S_v = P_S_v + proyeccion_ortogonal_de_v_a_S_un_generador(v, u, producto_interno_canonico)  \n",
        "  return P_S_v\n"
      ],
      "metadata": {
        "id": "ySsM8G-KClGR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Distancia**"
      ],
      "metadata": {
        "id": "52Bu0PrlZh8w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def distancia_entre_funciones(f1, f2, producto_interno, G: Matrix = None):\n",
        "  f = f1 - f2\n",
        "  d = norma(f, producto_interno)\n",
        "  return d"
      ],
      "metadata": {
        "id": "pCBJJnwcC0aJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ángulo** "
      ],
      "metadata": {
        "id": "5S54mqIOjuOg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def angulo(x: Matrix, y: Matrix, producto_interno, G: Matrix=None):\n",
        "    return acos(producto_interno(x, y, G) / (norma(x, producto_interno, G) * norma(y, producto_interno, G)))"
      ],
      "metadata": {
        "id": "ycrJC5d_pvGR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Subespacios**"
      ],
      "metadata": {
        "id": "serb46aa-3Dq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Recuerdo:\n",
        "*   $rango(A)$ = $dim(col(A))$ = $dim(col(A^T))$.\n",
        "*   $dim(nul(A))$ = $n$ − $rango(A)$ = $n$ − $dim(col(A)) \\quad$ donde $\\quad n$ = cantidad de columnas de $A$ \n",
        "\n",
        "*   $dim(nul(A^T))$ = $m$ − $dim(col(A^T)) \\quad$ donde $\\quad m$ = cantidad de filas de $A$ \n",
        "\n",
        "_________________\n",
        "\n",
        "Vale que $nul(A) = col(A^T)^\\perp$. Entonces: $$\\mathbb R^n = nul(A) \\oplus col(A^T).$$\n",
        "\n",
        "También vale que $nul(A^T) = col(A)^\\perp$. Entonces: $$\\mathbb R^m = nul(A^T) \\oplus col(A).$$\n"
      ],
      "metadata": {
        "id": "HYOLyYcg_CID"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "CZj_rrSUCsct"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Recuerdo:\n",
        "\n",
        "$Bx=v$ tiene solución si y solamente si $v ∈ col(B)$\n",
        "\n",
        "*   $Bx=v$ tiene solución única $<=>$ las columnas de A forman un conjunto LI $<=>$ $Nul(A)$ = 0 \n",
        " \n",
        "*   $Bx=v$ tiene $\\infty$ soluciones $<=>$ las columnas de A forman un conjunto LD $<=>$ $Nul(A)$ $\\neq$ 0 "
      ],
      "metadata": {
        "id": "48tJVTgACrlk"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "EhxP9eTDDiGC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "'''  \n",
        "  A.nullspace() -> devuelve el espacio nulo de A \n",
        "  A.columnspace() -> devuelve el espacio columna de A\n",
        "  A.T.columnspace() -> devuelve el espacio columna de A traspuesta\n",
        "  A.T.nullspace() -> devuelve el espacio nulo de A traspuesta\n",
        "  n, m = A.shape -> cantidad de filas y columnas de la matriz\n",
        "'''\n",
        "\n",
        "'''\n",
        "    S: lista de los vectores que generan al subespacio S\n",
        "    Los pivotes empiezan en 0 (por ej: la segunda columna figuraría con el pivote 1)\n",
        "'''\n",
        "def algoritmo_espacio_columna(S: List[Matrix]): #Encuentra el espacio columna de un subespacio\n",
        "    B_S = Matrix.hstack(*S)\n",
        "    E_S, pivotes_S = B_S.rref()\n",
        "    S_li = []\n",
        "    for pivote in pivotes_S:\n",
        "        S_li.append(S[pivote])        #De la matriz original\n",
        "    return S_li, pivotes_S #devuelve la matriz con los vectores que generan el espacio columna y los índices de los pivotes.    \n",
        "\n",
        "def algoritmo_espacio_filas(S: List[Matrix]): #Encuentra el espacio fila de un subespacio\n",
        "    B_S = Matrix.hstack(*S).T\n",
        "    E_S, pivotes_S = B_S.rref()\n",
        "    S_li = []\n",
        "    for pivote in pivotes_S:\n",
        "        S_li.append((E_S[pivote,:]).T) #De la matriz escalonada\n",
        "    return S_li, pivotes_S #devuelve la matriz con los vectores que generan el espacio fila y los índices de los pivotes.     \n",
        "\n",
        "def dos_subespacios_generan_el_mismo_subespacio(S1: List[Matrix], S2: List[Matrix]):\n",
        "    \n",
        "    S1_li, pivotes_S1 = algoritmo_espacio_columna(S1)\n",
        "    S2_li, pivotes_S2 = algoritmo_espacio_columna(S2)\n",
        "    \n",
        "    B_S1_li = Matrix.hstack(*S1_li)\n",
        "    B_S2_li = Matrix.hstack(*S2_li)\n",
        "    \n",
        "    B = Matrix.hstack(B_S1_li, B_S2_li)\n",
        "    _, pivotes_B = B.rref()\n",
        "    \n",
        "    return len(pivotes_B) == len(pivotes_S1) and len(pivotes_B) == len(pivotes_S2)\n"
      ],
      "metadata": {
        "id": "s8B9gaDdC58S"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Mínimos cuadrados**"
      ],
      "metadata": {
        "id": "ws51C0ncE34U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#A.pinv() -> pseudoinversa \n",
        "\n",
        "def solucion_por_minimos_cuadrados(A, b):\n",
        "  ATA = (A.T)*A\n",
        "  ATb = (A.T)*b\n",
        "  sol, sp, generadores = gauss_jordan_con_generadores(ATA, ATb)\n",
        "  return sp, generadores\n",
        "\n",
        "def error_cuadratico(b, A, x):\n",
        "  return (b - A*x).norm()**2\n",
        "\n",
        "def solucion_norma_minima(A, sp):\n",
        "  filA = A.T.columnspace()\n",
        "  MfilA = Matrix.hstack(*filA)\n",
        "  sol, x_coord, gen = gauss_jordan_con_generadores(A*MfilA, A*sp)\n",
        "  x_hat = Matrix.hstack(*filA)*x_coord #la solucion de Ax = b de norma mínima\n",
        "  norma = x_hat.norm() #la norma\n",
        "  return x_hat, norma\n",
        "\n",
        "def solucion_por_minimos_cuadrados_rango_max(A, b):\n",
        "  A_MP = A.pinv() #matriz pseudoinversa de Moore-Penrose\n",
        "  x_hat = A_MP * b #solución por mínimos cuadrados de Ax=b\n",
        "  return x_hat"
      ],
      "metadata": {
        "id": "Nbm2Edu9Rd3S"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Base Ortogonal**"
      ],
      "metadata": {
        "id": "7oS9KEoMsiGK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def normalizar_base(v1,v2,producto_interno, G: Matrix = None): #pi personalizado\n",
        "\n",
        "  v1_hat = v1 / norma(v1,producto_interno, G)\n",
        "  \n",
        "  aux = v2 - producto_interno(v2,v1, G) / norma(v1,producto_interno, G)**2 * v1\n",
        "  v2_hat = aux / norma(aux, producto_interno, G)\n",
        "\n",
        "  return v1_hat, v2_hat\n",
        "\n",
        "#GramSchmidt([v1, v2, v3, v4], orthonormal=True)\n",
        "\n",
        "def proyeccion_ortogonal_de_v_a_S_ortogonal(v: Matrix, B: List[Matrix]):\n",
        "  m, n = v.shape\n",
        "  P_S_v = zeros(m, n)\n",
        "  for i in range(len(B)):\n",
        "    u = B[i]\n",
        "    P_S_v = P_S_v + proyeccion_ortogonal_de_v_a_S_un_generador(v, u, producto_interno_canonico)  \n",
        "  return P_S_v\n",
        "\n",
        "def QR(A):\n",
        "  B = A.columnspace()\n",
        "  Q = GramSchmidt(B, orthonormal='True') #esta es Q\n",
        "  MQ = Matrix.hstack(*Q)\n",
        "  MR = MQ.gauss_jordan_solve(A)[0]\n",
        "  return MQ, MR"
      ],
      "metadata": {
        "id": "DkFDH40aDq7w"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Específico**"
      ],
      "metadata": {
        "id": "2NTL8vA8FqxC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Polinomio Característico**"
      ],
      "metadata": {
        "id": "OsIRns-G6EIy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "El polinomio $\\chi_A(x) = det(A-xI)$ se llama el polinomio característico de $A$.\n",
        "\n",
        "Al factorizarse, el polinomio característico queda escrito como $$\\chi_A = (x-\\lambda_1)^{m_{\\lambda _1}}\\dots(x-\\lambda_n)^{m_{\\lambda _n}}$$ donde $m_{\\lambda _n}$ se llama la multiplicidad algebraica de $\\lambda$.\n"
      ],
      "metadata": {
        "id": "niBXy-im6MNK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def chi(matriz): #Polinomio Caracteristico\n",
        "  n, m = matriz.shape\n",
        "  assert n == m, \"La matriz tiene que ser cuadrada\"\n",
        "  I = eye(n)\n",
        "  x = Symbol('x')\n",
        "  chi_matriz = (matriz - x*I).det()\n",
        "  return chi_matriz"
      ],
      "metadata": {
        "id": "O2T5DD_o6Pwr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Autovalores y Autovectores**"
      ],
      "metadata": {
        "id": "SZ5zncAu6XOR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sea $A \\in \\mathbb K^{n \\times n}$. Entonces $\\lambda \\in \\mathbb K$ es un autovalor de $A$ si existe un vector no nulo $x \\in \\mathbb K^n$ tal que $Ax = \\lambda x$. En tal caso, el vector $x$ se llama un autovector de $A$ correspondiente al autovalor $\\lambda$. El conjunto de todos los autovalores de $A$ es el espectro de $A$, y se designa como $\\sigma(A)$.\n",
        "\n",
        "$$\\sigma(A)=\\left\\{\\lambda\\in\\mathbb{R}: \\chi_A(\\lambda)=0\\right\\}.$$\n",
        "\n",
        "Si $A$ es inversible, entonces: $$\\sigma(A^{-1})= \\{\\lambda^{-1} :  \\lambda \\in\\sigma(A)\\}.$$\n",
        "\n",
        "El subespacio $nul(A - \\lambda I)$ se denomina el autoespacio de $A$ correspondiente al autovalor $\\lambda$; su dimensión se denominada la multiplicidad geométrica de $\\lambda$: $$\\mu(\\lambda) = dim(nul(A-\\lambda I)).$$\n",
        "\n",
        "Todo conjunto formado por autovectores de $A$ correspondientes a autovalores de $A$ es un conjunto linealmente independiente.\n",
        "\n",
        "Notar que $$\\sigma\\left(N^k\\right)=\\left\\{\\lambda^k: \\lambda\\in\\sigma(N)\\right\\}.$$\n",
        "\n",
        "**Tip.** Si todas las filas de una matriz suman lo mismo, entonces esa suma es un autovalor, y un autovector asociado a ese autovalor es el $\\begin{bmatrix}1&1&1\\end{bmatrix}$"
      ],
      "metadata": {
        "id": "QLL756eh6cyx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#matriz.eigenvals() #autovalores y multiplicidades algebraicas\n",
        "#matriz.eigenvects() #autovalores, multiplicidades algebraicas, autoespacios\n",
        "\n",
        "def base_autovects(A): #Base autovectores: P\n",
        "  autovects =  A.eigenvects()\n",
        "  m = len(autovects)\n",
        "  X = list()\n",
        "  for i in range(m):\n",
        "    X.append(Matrix.hstack(*autovects[i][2]))\n",
        "  P = Matrix.hstack(*X)\n",
        "  return P\n",
        "\n",
        "def autovals_and_autospaces(A):\n",
        "  n, m = A.shape\n",
        "  assert n == m, \"A tiene que ser cuadrada\"\n",
        "\n",
        "  identity_mat = eye(n) # Matriz identidad en n x n\n",
        "\n",
        "  l = symbols('\\lambda')\n",
        "  polyA = (A - l * identity_mat).det()\n",
        "\n",
        "  avas = roots(polyA,l)\n",
        "  avas = list(avas.keys())\n",
        "\n",
        "  aves = {ava: (A-ava*identity_mat).nullspace() for ava in avas}\n",
        "\n",
        "  return avas, aves"
      ],
      "metadata": {
        "id": "JWcikLJd634N"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Diagonalización**\n"
      ],
      "metadata": {
        "id": "nu0TMwoSe2j7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Dos matrices $A$ y $B \\in \\mathbb K^{n \\times n}$ son semejantes si existe una matriz inversible $P \\in \\mathbb K^{n \\times n}$ tal que $P^{-1}AP = B$. El producto $P^{-1}AP$ se denomina transformación de semejanza de $A$.\n",
        "\n",
        "El polinomio característico es invariante por transformaciones de semejanza. Es decir, si $A$ y $B$ son semejantes, entonces sus polinomios característicos son idénticos.\n",
        "\n",
        "Una matriz $A \\in \\mathbb K^{n \\times n}$ es diagonalizable si $A$ es semejante a una matriz diagonal $\\Lambda = diag(\\lambda_1, \\dots, \\lambda_n)$, es decir \\begin{align}\n",
        "P^{-1}&AP \\quad\\quad  = \\space\\space\\space\\Lambda \\\\\n",
        "PP^{-1}&APP^{-1} \\space = P \\Lambda P^{-1}\\\\\n",
        "&A \\quad\\quad\\space\\space\\space   = P \\Lambda P^{-1}\n",
        "\\end{align}\n",
        "\n",
        "Si $A$ es diagonalizable, entonces: $$det(A) = \\prod_{i=1}^{m}\\lambda_i^{\\mu(\\lambda_i)} \\quad y \\quad tr(A) = \\sum_{i=1}^m \\mu(\\lambda_i)\\lambda_i.$$\n",
        "\n",
        "Notar que $A^2 = P \\Lambda P^{-1}P \\Lambda P^{-1} = P\\Lambda I\\Lambda P^{-1} = P\\Lambda^2P^{-1}$. Es decir $$A^n = P\\Lambda^nP^{-1}$$\n",
        "\n",
        "Además, como $A.v = \\lambda v$, con $v$ autovector $A$, entonces $$A^nv = \\lambda ^nv$$\n",
        "\n",
        "* Sea $A \\in \\mathbb K^{n \\times n}$. Si $|\\sigma(A)| = n$, entonces $A$ es diagonalizable.\n",
        "* Para que $A$ sea diagonalizable, sus multiplicidades geométrica y algebraica deben coincidir.\n",
        "\n",
        "___\n",
        "**Hallar las matrices $P$ y $\\Lambda$:**\n",
        "\n",
        "* Se halla el polinomio característico de $A$: $$\\chi_A(x) = \\det(A - xI).$$\n",
        "\n",
        "* Se halla el espectro de $A$: \n",
        "$$\\sigma(A)=\\left\\{\\lambda\\in\\mathbb{R}: \\chi_A(\\lambda)=0\\right\\}.$$\n",
        "\n",
        "* Se halla el subespacio asociado a cada $\\lambda$: $$\\mathbb S_\\lambda = nul(A - \\lambda I).$$\n",
        "$\\rightarrow$ Si sumo todas las multiplicidades geométricas, y me da menor a $n$, entonces $A$ no es diagonalizable\n",
        "\n",
        "* Se arman las matrices: $$\\Lambda = diag(\\lambda_1, \\dots, \\lambda_n), \\quad P = [\\mathbb S_1 \\dots \\mathbb S_n]$$\n",
        "$\\rightarrow$ el orden en el que colocar los $\\lambda$ es decreciente en valor de módulo, y en caso de tener módulos iguales, primero el positivo.\n",
        "\n",
        "___\n",
        "\n"
      ],
      "metadata": {
        "id": "SAF65k7Ye6nT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#P, Lambda = matriz.diagonalize() #P y Diagonal"
      ],
      "metadata": {
        "id": "h86ZCsbVfQg7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Polinomios y Matrices**"
      ],
      "metadata": {
        "id": "XJs15tqPfGXj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sean $A\\in \\mathbb K^{n \\times n}$ y $p \\in \\mathbb K_m[x]$, con $p(x)=\\sum_{k=0}^m b_kx^k$, entonces: $$p(A) = \\sum_{k=0}^m b_kA^k,$$ donde $A^0 = I$.\n",
        "\n",
        "Si $p$ se factoriza como $p = p_1p_2$, entonces $p(A) = p_1(A)p_2(A)$. \n",
        "\n",
        "Notar que $$\\sigma\\left(p(A)\\right) = \\{p(\\lambda): \\lambda \\in \\sigma(A)\\}$$\n",
        "\n",
        "Además, $p(\\lambda)$ es un autovalor de $p(A)$ y que $v$ es un autovector de $p(A)$ correspondiente al autovalor $p(\\lambda)$.\n",
        "\n",
        "Por último, $nul(A-\\lambda I) \\subseteq nul\\left(p(A)- p(\\lambda)I\\right)$.\n",
        "\n",
        "Entonces vale que $$\\sigma\\left(N^k\\right)=\\left\\{\\lambda^k: \\lambda\\in\\sigma(N)\\right\\}.$$"
      ],
      "metadata": {
        "id": "K228d8rKfKE0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Proyectores**"
      ],
      "metadata": {
        "id": "JKHZa6Ml5qdA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Una matriz $A \\in \\mathbb K^{n \\times n}$ con espectro $\\sigma(A) = \\{\\lambda_1, \\dots, \\lambda_m\\}$ es diagonalizable sii existen matrices $\\{G_1, \\dots, G_m\\}$ tales que $A = \\lambda_1 G_1 + \\dots + \\lambda_n G_m$ **(descomposición espectral de $A$)**.\n",
        "\n",
        "Las $G_i$ se llaman los proyectores espectrales asociados.\n",
        "\n",
        "\n",
        "**Propiedades**\n",
        "\n",
        "* $G_i$ es la proyección sobre $nul(A - \\lambda_i I)$ en la dirección de $col(A - \\lambda_i I)$.\n",
        "\n",
        "$\\rightarrow$ Notar que $Nul(A-\\lambda_1I) = Col(G_i)$,\n",
        "\n",
        "$\\quad\\quad\\quad\\quad\\quad Col(A-\\lambda_1I) = Nul(G_i)$\n",
        "\n",
        "* $G_iG_j = 0$ para $i \\neq j$\n",
        "* $G_1 + \\dots + G_m = I$\n",
        "\n",
        "Vale que $$A^n = \\lambda_1^nG_1 + \\dots + \\lambda_m^nG_m$$\n",
        "\n",
        "**Hacer la descomposición espectral de $A$**\n",
        "\n",
        "\\begin{align}\n",
        "A &= \\underbrace{\\begin{bmatrix}X_1&\\dots&X_m\\end{bmatrix}}_P \\underbrace{\\begin{bmatrix}\\lambda_1 I_{\\mu(\\lambda_1)}\\\\&\\ddots\\\\&&\\lambda_m I_{\\mu(\\lambda_m)}\\end{bmatrix}}_\\Lambda \\underbrace{\\begin{bmatrix}Y_1^T\\\\\\vdots\\\\Y_m^T\\end{bmatrix}}_{P^{-1}}\\\\\n",
        "&= \\begin{bmatrix}\\lambda_1X_1&\\dots&\\lambda_mX_m\\end{bmatrix} \\begin{bmatrix}Y_1^T\\\\\\vdots\\\\Y_m^T\\end{bmatrix}\\\\\\\\\n",
        "&= \\lambda_1 \\underbrace{X_1 Y_1^T}_{G_1} + \\dots + \\lambda_1 \\underbrace{X_m Y_m^T}_{G_m}\n",
        "\\end{align}"
      ],
      "metadata": {
        "id": "8ONq_TEx50Ka"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def DS(matriz): #Autovalores y proyectores\n",
        "  autovects =  matriz.eigenvects()\n",
        "  m = len(autovects)\n",
        "  X = list()\n",
        "  for i in range(m):\n",
        "    X.append(Matrix.hstack(*autovects[i][2]))\n",
        "  P = Matrix.hstack(*X)\n",
        "  IP = P.inv()\n",
        "  k = 0\n",
        "  mu = list()\n",
        "  mu.append(0)\n",
        "  for i in range(m): \n",
        "    k = k + autovects[i][1]\n",
        "    mu.append(k)\n",
        "  Y = list()\n",
        "  for k in mu[0:m]:\n",
        "    Y.append(IP[mu[k]:mu[k+1], :])\n",
        "  G = list()\n",
        "  for j in range(len(X)):\n",
        "    G.append(simplify(autovects[j][0]))\n",
        "    G.append(simplify(X[j]*Y[j]))\n",
        "  return(G)"
      ],
      "metadata": {
        "id": "FXSLjUBa6B34"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Limite**"
      ],
      "metadata": {
        "id": "dal1xqhr8zay"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "La norma Frobenius $\\|\\cdot\\|_F: \\mathbb R^{n \\times n} → \\mathbb R^+$ es la norma inducida por el producto interno canónico en $\\mathbb R^{n \\times n}$. Esto es, para cada $A \\in \\mathbb R^{n \\times n}$ vale que $$\\|A\\|_F = \\sqrt{tr(A^TA)} = \\sqrt{\\sum_{i=1}^n\\sum_{j=1}^n a_{ij}^2}$$\n",
        "\n",
        "Se dice que la sucesión $(A^k)_{k \\in \\mathbb N}$ es convergente si existe una matriz $A^* \\in \\mathbb R^{n \\times n}$ tal que $$\\lim_{k \\rightarrow \\infty} \\|A^k - A^*\\|_F = 0.$$\n",
        "\n",
        "Se escribe entonces que $\\lim_{k→∞}A^k = A^*$, y se dice que $A^k$ converge a $A^*$.\n",
        "\n",
        "Si $A$ es una matriz diagonalizable, el comportamiento asintótico de la sucesión $(A^k)_{k \\in \\mathbb N}$ está gobernado por el radio espectral de $A$ que se define mediante $$\\rho(A) = max\\{|\\lambda|: \\lambda \\in \\sigma(A)\\}$$\n",
        "\n",
        "* Si $\\rho(A) < 1$, entonces $\\lim_{k→∞}A^k = 0$.\n",
        "* Si $\\rho(A) > 1$, entonces $\\lim_{k→∞}\\|A^k\\|_F = +\\infty$.\n",
        "* Si $\\rho(A) = 1$ y $-1 \\notin\\sigma(A)$, entonces $\\lim_{k→∞}A^k = G_1$.\n",
        "* Si $\\rho(A) = 1$ y $-1 \\in\\sigma(A)$, entonces las sucesiones $A^{2k}$ y$A^{2k-1}$ son convergentes y $\\lim_{k→∞}A^{2k} \\neq \\lim_{k→∞}A^{2k-1}$\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "Si $(A^k)_{k \\in \\mathbb N}$ es convergente, entonces $$\\lim_{k→∞}A^kx = \\left(\\lim_{k→∞}A^k\\right)x.$$"
      ],
      "metadata": {
        "id": "2bAJUHImHBdr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def limite(A):\n",
        "  m = len(A.nullspace()) + len(A.columnspace())\n",
        "  n = Symbol('n')\n",
        "  A_n = A**n\n",
        "  A_infty = zeros(m, m)\n",
        "  for i in range(m):\n",
        "      for j in range(m):\n",
        "          A_infty[i,j] = simplify(limit_seq(A_n[i,j]))\n",
        "  return(A_infty) \n",
        "\n",
        "#Esta función calcula el limite de la sucesión A^n \n",
        "#(casi seguro que para matrices diagonalizables)"
      ],
      "metadata": {
        "id": "sQG3-W-o82zb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Matrices Nilpotentes**"
      ],
      "metadata": {
        "id": "2EodMwpnMdF-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sea $N\\in\\mathbb{R}^{n\\times n}$. Decimos que $N$ es una matriz nilpotente de índice $k$ si\n",
        "$$N^k=0\\,\\mbox{ pero }\\, N^{k-1}\\neq 0.$$\n",
        "Notar que si $N$ es nilpotente de índice $k$ y $N\\neq 0$, entonces $N$ no es diagonalizable.\n",
        "\n",
        "**Teorema de Hamilton-Cayley**. Si $A\\in\\mathbb{R}^{n\\times n}$, entonces $\\chi_A(A)=0$.\n",
        "\n",
        "**Corolario**. Si $\\sigma(A)=\\{\\lambda\\}$, $\\chi_A(x)=(-1)^n(x-\\lambda)^n$. \n",
        "\n",
        "Esto implica que \n",
        "$$(A-\\lambda I)^n=0.$$\n",
        "Esto significa que la matriz $N=A-\\lambda I$ es nilpotente.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "Sea $N$ una matriz nilpotente de índice $2$. Esto significa que $N^2=0$ pero $N\\neq 0$. Elegimos $v\\notin{\\rm nul}(N)$ y formamos la cadena de Jordan\n",
        "$$\\left\\{Nv,v\\right\\}.$$\n",
        "Observamos que\n",
        "\\begin{align*}\n",
        "N\\begin{bmatrix}Nv&v\\end{bmatrix}=\\begin{bmatrix}0&Nv\\end{bmatrix}=\\begin{bmatrix}Nv&v\\end{bmatrix}\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}.\n",
        "\\end{align*}\n",
        "Sea $N$ una matriz nilpotente de índice $3$. Esto significa que $N^3=0$ pero $N^2\\neq 0$. Elegimos $v\\notin{\\rm nul}(N^2)$ y formamos la cadena de Jordan\n",
        "$$\\left\\{N^2v,Nv,v\\right\\}.$$\n",
        "Observamos que\n",
        "\\begin{align*}\n",
        "N\\begin{bmatrix}N^2v&Nv&v\\end{bmatrix}=\\begin{bmatrix}0&N^2v&Nv\\end{bmatrix}=\\begin{bmatrix}N^2v&Nv&v\\end{bmatrix}\\begin{bmatrix}0&1&0\\\\0&0&1\\\\0&0&0\\end{bmatrix}.\n",
        "\\end{align*}\n",
        "\n",
        "Y así con cada índice $\\dots$"
      ],
      "metadata": {
        "id": "3IUc6RlFMj0g"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Matrices no diagonalizables**"
      ],
      "metadata": {
        "id": "vmECR4-76asX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Una matriz $A$ no es diagonalizable si:\n",
        "* No tiene suficientes raíces reales.\n",
        "* Algún autoespacio no tiene suficientes autovectores linealmente independientes.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "vjgBOGLr6oNN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Morfología de las pequeñas matrices no diagonalizables**"
      ],
      "metadata": {
        "id": "-xMn6AfnA_bT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Toda matriz $A$ que no sea diagonalizable es semejante a una de las siguientes matrices: \n"
      ],
      "metadata": {
        "id": "sCoWFuAKBIAS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**$$\\underline{\\text{En } \\mathbb R^{2 \\times 2}}:$$**\n",
        "\n",
        "1.  **Rotaciones seguidas de cambio de escala**\n",
        "\n",
        "Matrices de la forma\n",
        "$$\\begin{bmatrix}a&b\\\\-b&a\\end{bmatrix},$$\n",
        "donde $a,b\\in\\mathbb{R}$ y $b\\neq 0$.\n",
        "\n",
        "La matriz no es diagonalizable porque le faltan autovalores reales.\n",
        "\n",
        "Notar que la matriz puede escribirse como: $$\\underbrace{\\rho}_{\\text{cambio de escala}} \\underbrace{\\begin{bmatrix}\\cos\\theta&-\\sin\\theta\\\\\\sin\\theta&\\cos\\theta\\end{bmatrix}}_{\\text{rotacion}},$$\n",
        "\n",
        "donde $\\rho > 0$, y $\\theta \\neq k \\pi$ con $k \\in \\mathbb Z$.\n",
        "\n",
        "También puede escribirse como:$$\\underbrace{\\sqrt{a^2+b^2}}_{\\text{cambio de escala}} \\underbrace{\\begin{bmatrix}\\frac{a}{\\sqrt{a^2+b^2}}&\\frac{b}{\\sqrt{a^2+b^2}}\\\\-\\frac{b}{\\sqrt{a^2+b^2}}&\\frac{a}{\\sqrt{a^2+b^2}}\\end{bmatrix}}_{\\text{rotacion}},$$\n",
        "\n",
        "2. **Bloques de Jordan**\n",
        "\n",
        "Matrices de la forma: $$\\begin{bmatrix}\\lambda&1\\\\0&\\lambda\\end{bmatrix},$$\n",
        "donde $\\lambda\\in\\mathbb{R}.$\n",
        "\n",
        "La matriz no es diagonalizable porque no me alcanzan los autovectores linealmente independientes para diagonalizar la matriz.\n",
        "\n"
      ],
      "metadata": {
        "id": "KOS-PhXIGi8O"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**$$\\underline{\\text{En } \\mathbb R^{3 \\times 3}}:$$**\n",
        "\n",
        "1. **Bloques de Jordan**\n",
        "\n",
        "Matrices de la forma: $$\\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&1\\\\0&0&\\lambda\\end{bmatrix},$$\n",
        "donde $\\lambda\\in\\mathbb{R}.$\n",
        "\n",
        "La matriz no es diagonalizable porque $\\mu(\\lambda) = 1$ y $m(\\lambda) = 3$.\n",
        "\n",
        "2. $ $\n",
        "\n",
        "Matrices de la forma: $$\\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&0\\\\0&0&\\lambda\\end{bmatrix},$$\n",
        "donde $\\lambda\\in\\mathbb{R}.$\n",
        "\n",
        "La matriz no es diagonalizable porque $\\mu(\\lambda) = 2$ y $m(\\lambda) = 3$.\n",
        "\n",
        "3. $ $\n",
        "\n",
        "Matrices de la forma: $$\\begin{bmatrix}\\lambda_1&1&0\\\\0&\\lambda_1&0\\\\0&0&\\lambda_2\\end{bmatrix},$$\n",
        "donde $\\lambda_1,\\lambda_2\\in\\mathbb{R}$ y $\\lambda_1 \\neq \\lambda_2.$\n",
        "\n",
        "La matriz no es diagonalizable porque $\\mu(\\lambda_1) = 1$ y $m(\\lambda_1) = 2$.\n",
        "\n",
        "4. $ $\n",
        "\n",
        "Matrices de la forma: $$\\begin{bmatrix}a&b&0\\\\-b&a&0\\\\0&0&\\lambda\\end{bmatrix},$$\n",
        "donde $a,b,\\lambda\\in\\mathbb{R}$ y $b\\neq 0$.\n",
        "\n",
        "La matriz no es diagonalizable porque le faltan autovalores reales.\n",
        "\n",
        "\n",
        "$→$ **Tip: para saber cuántos $1$'s tiene el bloque de jordan, se hace $$m(\\lambda) - \\mu(\\lambda).$$**"
      ],
      "metadata": {
        "id": "MbVl4qAMGfrR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "####**Hallar la forma canónica de Jordan**"
      ],
      "metadata": {
        "id": "4d10sKb8BPcD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\bullet$ Caso $A$ con autovalores complejos.\n",
        "\n",
        "\n",
        "* Hallo los autovalores y sus autovectores asociados.\n",
        "\n",
        "$\\quad$Observación: Si $z\\in\\mathbb{C}^n$ es un autovector asociado a $a+bi$, entonces $\\overline{z}$ es un autovector asociado al autovalor $a-bi$.\n",
        "\n",
        "* Descompongo uno de los autovectores (me conviene elegir el positivo) como: $$z=x+iy,$$ entonces$$P=\\begin{bmatrix}x&y\\end{bmatrix}$$\n",
        "\n",
        "* Y $\\Lambda$ se halla escribiendo a qué matriz es semejante."
      ],
      "metadata": {
        "id": "r-KDxLOdCiCy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\bullet$ Caso $A \\in \\mathbb R^{2 \\times 2}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 2, \\mu(\\lambda) = 1.$\n",
        "\n",
        "1. Armar $$N=A-\\lambda I.$$\n",
        "2. Buscar $v\\notin{\\rm nul}(N)$. Por ejemplo, una fila.\n",
        "3. Se definen entonces\n",
        "$$P=\\begin{bmatrix}Nv&v\\end{bmatrix}, \\quad \\Lambda = \\begin{bmatrix}\\lambda&1\\\\0&\\lambda\\end{bmatrix}.$$"
      ],
      "metadata": {
        "id": "zORtLcIJ-5l7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 3, \\mu(\\lambda) = 1.$\n",
        "\n",
        "1. Armar $$N=A-\\lambda I.$$\n",
        "2. Buscar $v\\notin{\\rm nul}(N^2)$. Por ejemplo,\n",
        "una fila.\n",
        "4. Se definen entonces\n",
        "$$P=\\begin{bmatrix}N^2v&Nv&v\\end{bmatrix}, \\quad \\Lambda = \\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&1\\\\0&0&\\lambda\\end{bmatrix}.$$\n"
      ],
      "metadata": {
        "id": "oyHv8mhb_rP9"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 3, \\mu(\\lambda) = 2.$\n",
        "\n",
        "1. Armar $$N=A-\\lambda I.$$\n",
        "2. Buscar $v_1\\notin{\\rm nul}(N)$. Por ejemplo, una fila.\n",
        "3. Buscar $v_2\\in{\\rm nul}(N)\\setminus gen(Nv_1)$. Es decir, linealmente independiente con $Nv_1$.\n",
        "4. Se definen entonces\n",
        "$$P=\\begin{bmatrix}Nv_1&v_1&v_2\\end{bmatrix}, \\quad \\Lambda = \\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&0\\\\0&0&\\lambda\\end{bmatrix}.$$"
      ],
      "metadata": {
        "id": "STi2ErSDBvVd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda_1, \\lambda_2\\}, m(\\lambda_1) = 2, \\mu(\\lambda_1) = 1$\n",
        "\n",
        "1. Armar $$N_1=A-\\lambda_1 I,\\quad N_2=A-\\lambda_2 I$$\n",
        "2. Buscar $v_1\\in{\\rm nul}(N_1^2)\\setminus {\\rm nul}(N_1)$.\n",
        "3. Buscar $v_2\\in{\\rm nul}(N_2)$.\n",
        "4. Se definen entonces\n",
        "$$P=\\begin{bmatrix}N_1v_1&v_1&v_2\\end{bmatrix}, \\quad \\Lambda = \\begin{bmatrix}\\lambda_1&1&0\\\\0&\\lambda_1&0\\\\0&0&\\lambda_2\\end{bmatrix}.$$"
      ],
      "metadata": {
        "id": "CL_2Z7CPGStm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#P, B = matriz.jordan_form()"
      ],
      "metadata": {
        "id": "Egcw4AqwYZOV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Sistemas de Ecuaciones Diferenciales**"
      ],
      "metadata": {
        "id": "hb13VParH9gj"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Si $\\lambda \\in \\sigma(A)$ y $v \\in nul(A-\\lambda I)$, entonces la función $Y(t) = e^{\\lambda t}v$ es solución del sistema $Y' = AY$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A$ diagonalizable**\n",
        "\n",
        "Se tiene $A = P\\Lambda P^{-1}$ con $P = \\begin{bmatrix}v_1 &\\dots&v_n\\end{bmatrix}$ y $\\Lambda = \\begin{bmatrix}\\lambda_1\\\\&\\ddots\\\\&&\\lambda_n\\end{bmatrix}$.\n",
        "\n",
        "La solución general del sistema $Y' = AY$ es $$Y = \\sum_{j=1}^n c_j e^{\\lambda_j t} v_j.$$\n",
        "\n",
        "En particular $\\{e^{\\lambda_1 t} v_1, \\dots, e^{\\lambda_n t} v_n\\}$ es un conjunto fundamental de soluciones del sistema $Y' = AY$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A$ con autovalores complejos**\n",
        "\n",
        "Si $a + bi$ es un autovalor de la matriz $A\\in \\mathbb R^{n \\times n}$ y $x + iy$ un autovector de $A$ asociado al autovalor $a+bi$, entonces $\\{e^{at} \\cos(bt)x - e^{at} \\sin(bt)y, e^{at} \\cos(bt)y + e^{at} \\sin(bt)x\\}$ es un conjunto de soluciones reales linealmente independiente del sistema $Y' = AY$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A \\in \\mathbb R^{2 \\times 2}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 2, \\mu(\\lambda) = 1.$**\n",
        "\n",
        "Se tiene $A = P\\Lambda P^{-1}$ con $P = \\begin{bmatrix}v_1 &v_2\\end{bmatrix}$ y $\\Lambda = \\begin{bmatrix}\\lambda&1\\\\0&\\lambda\\end{bmatrix}$.\n",
        "\n",
        "Sistema fundamental de soluciones de $Y' = AY$: $\\{e^{\\lambda t}v_1, e^{\\lambda t}(tv_1 + v_2)\\}$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 3, \\mu(\\lambda) = 1.$**\n",
        "\n",
        "Se tiene $A = P\\Lambda P^{-1}$ con $P = \\begin{bmatrix}v_1 &v_2&v_3\\end{bmatrix}$ y $\\Lambda = \\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&1\\\\0&0&\\lambda\\end{bmatrix}$.\n",
        "\n",
        "Sistema fundamental de soluciones de $Y' = AY$: $\\{e^{\\lambda t}v_1, e^{\\lambda t}(tv_1 + v_2), e^{\\lambda t}(\\frac{t^2}{2}v_1 + tv_2 + v_3)\\}$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda\\}, m(\\lambda) = 3, \\mu(\\lambda) = 2.$**\n",
        "\n",
        "Se tiene $A = P\\Lambda P^{-1}$ con $P = \\begin{bmatrix}v_1 &v_2&v_3\\end{bmatrix}$ y $\\Lambda = \\begin{bmatrix}\\lambda&1&0\\\\0&\\lambda&0\\\\0&0&\\lambda\\end{bmatrix}$.\n",
        "\n",
        "Sistema fundamental de soluciones de $Y' = AY$: $\\{e^{\\lambda t}v_1, e^{\\lambda t}(tv_1 + v_2), e^{\\lambda t}v_3\\}$.\n",
        "\n",
        "$ \\\\ $\n",
        "\n",
        "$\\quad$ **$\\bullet$ Caso $A \\in \\mathbb R^{3 \\times 3}: \\sigma(A) = \\{\\lambda_1, \\lambda_2\\}, m(\\lambda_1) = 2, \\mu(\\lambda_1) = 1.$**\n",
        "\n",
        "Se tiene $A = P\\Lambda P^{-1}$ con $P = \\begin{bmatrix}v_1 &v_2&v_3\\end{bmatrix}$ y $\\Lambda = \\begin{bmatrix}\\lambda_1&1&0\\\\0&\\lambda_1&0\\\\0&0&\\lambda_2\\end{bmatrix}$.\n",
        "\n",
        "Sistema fundamental de soluciones de $Y' = AY$: $\\{e^{\\lambda_1 t}v_1, e^{\\lambda_1 t}(tv_1 + v_2), e^{\\lambda_2 t}v_3\\}$.\n"
      ],
      "metadata": {
        "id": "06nEqQIJIFWS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Ejercicios**"
      ],
      "metadata": {
        "id": "-5wQaZTfGEHK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Ejercicios Generales**"
      ],
      "metadata": {
        "id": "Ybrp4YfFGJNF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Sea $A \\in \\mathbb R^{3 \\times 3}$, $A = \\begin{bmatrix}1&0&0\\\\-6&4&-3\\\\k&-2&3\\end{bmatrix}$. Hallar $k \\in \\mathbb R$ para que $A$ sea diagonalizable. Para el valor de $k$ hallado, dar una matriz inversible $P$ y una matriz diagonal $\\Lambda \\quad / A = P\\Lambda P^{-1}$"
      ],
      "metadata": {
        "id": "2QYvHULtkKbr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "k = Symbol('k')\n",
        "A = Matrix([[1, 0, 0],\n",
        "            [-6, 4, -3],\n",
        "            [k, -2, 3]])\n",
        "roots((chi(A)).factor())\n",
        "#para que A sea diagonalizable, entonces el autovalor doble debe tener asociado un subespacio de dimensión doble (m = μ)\n",
        "#Averiguo nul(A-1*eye(3,3)) -> lo hago a mano porque en Python no se puede\n",
        "\"\"\"\n",
        "A-I = Matrix([[ 0,  0,  0],\n",
        "              [-6,  3, -3],\n",
        "              [ k, -2,  2]])\n",
        "    = Matrix([[ 0,      0,      0],\n",
        "              [-2,      1,     -1],\n",
        "              [ 0, -12+3k,  12-3k]]) -> si la fila no se anula, rango(A) = 2, nul(A) = 1\n",
        "-> La fila se tiene que anular: k = 4\n",
        "\"\"\"\n",
        "A = A.subs(k, 4)\n",
        "P, Lambda = A.diagonalize()"
      ],
      "metadata": {
        "id": "dQ1DpE8ul3Vj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Sea $A \\in \\mathbb R^{4 \\times 4} / Nul(A) = gen\\left\\{\\begin{bmatrix}1&0&-1&0\\end{bmatrix}^T,\\begin{bmatrix}0&0&0&1\\end{bmatrix}^T\\right\\}, Nul(A-3I) = gen\\left\\{\\begin{bmatrix}0&1&-1&0\\end{bmatrix}^T\\right\\}, Nul(A+2I) = gen\\left\\{\\begin{bmatrix}0&0&1&2\\end{bmatrix}^T\\right\\}$. ¿Es $A$ diagonalizable? Sin dar explícitamente la matriz $A$, calcular $A\\begin{bmatrix}0&2&-2&5\\end{bmatrix}^T$ y decidir si el sistema $Ax = \\begin{bmatrix}1&0&0&1\\end{bmatrix}^T$ tiene solución."
      ],
      "metadata": {
        "id": "J5GrdMSZzGxR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Veo que B = {[1 0 -1 0], [0 0 0 1], [0 1 -1 0], [0 0 1 2]} es una base de R4 formada por autovectores de A\n",
        "#Se que\n",
        "#A[1 0 -1 0] = [0 0 0 0]\n",
        "#A[0 0 0 1] = [0 0 0 0]\n",
        "#A[0 1 -1 0] = 3[0 1 -1 0]\n",
        "#A[0 0 1 2] = -2[0 0 1 2]\n",
        "B = [Matrix([1, 0, -1, 0]), Matrix([0,0,0,1]), Matrix([0,1, -1,0]), Matrix([0,0,1,2])]\n",
        "W = [Matrix([0, 0, 0, 0]), Matrix([0,0,0,0]), Matrix([0,3,-3,0]), Matrix([0,0,-2,-4])]\n",
        "S = [Matrix([0,2,-2,5])]\n",
        "A_T = matriz_tl_con_base_y_transformados(B, W)\n",
        "imagen_por_T_de_S_con_B_y_W(B, W, S)\n",
        "\n",
        "#Ax = b tiene sol si b pertenece a Col(A), Col(A) = {[0 1 -1 0], [0 0 1 2]} (el resto van al nulo)\n",
        "#Matrix.hstack(Matrix([0, 1, -1, 0]), Matrix([0, 0, 1, 2])).gauss_jordan_solve(Matrix([1, 0, 0, 1])) #no tiene sol"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 98
        },
        "id": "VXkadpHc0tEW",
        "outputId": "75f94806-4081-4f7e-b88f-3fc394a402ee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left[\\begin{matrix}0\\\\6\\\\-6\\\\0\\end{matrix}\\right]\\right]$",
            "text/plain": [
              "⎡⎡0 ⎤⎤\n",
              "⎢⎢  ⎥⎥\n",
              "⎢⎢6 ⎥⎥\n",
              "⎢⎢  ⎥⎥\n",
              "⎢⎢-6⎥⎥\n",
              "⎢⎢  ⎥⎥\n",
              "⎣⎣0 ⎦⎦"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sol, sp, gen = gauss_jordan_con_generadores(Matrix([[2,2,1]]), zeros(1))\n",
        "encontrar_vector_li_a_conjunto(gen)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "1NOX_wL0IMMU",
        "outputId": "9230c4b5-c5e5-43f9-d8cf-fb913dbcc791"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left[\\begin{matrix}-1\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}- \\frac{1}{2}\\\\0\\\\1\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\\\0\\end{matrix}\\right]\\right]$",
            "text/plain": [
              "⎡⎡-1⎤  ⎡-1/2⎤  ⎡1⎤⎤\n",
              "⎢⎢  ⎥  ⎢    ⎥  ⎢ ⎥⎥\n",
              "⎢⎢1 ⎥, ⎢ 0  ⎥, ⎢0⎥⎥\n",
              "⎢⎢  ⎥  ⎢    ⎥  ⎢ ⎥⎥\n",
              "⎣⎣0 ⎦  ⎣ 1  ⎦  ⎣0⎦⎦"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Hallar todos los valores de $a,b,c \\in \\mathbb R / A = \\begin{bmatrix}a&0\\\\b&c\\end{bmatrix}$ sea diagonalizable y $\\begin{bmatrix}1&1\\end{bmatrix}^T \\in Nul(A-2I)$. En cada caso, dar una base de $\\mathbb R^2$ formada por autovectores de $A$."
      ],
      "metadata": {
        "id": "6Bx56lUGAaql"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#se que 2 es autovalor de A, y uno de los autovectores asociados es [1 1]\n",
        "#Entonces A.v = 2.v\n",
        "\"\"\"\n",
        "          [[a, 0],[b, c]].[1,1] = 2.[1,1]\n",
        "          [a, b+c] = [2,2] -> a = 2, b = 2-c\n",
        "          A = [[2,  0],\n",
        "               [2-c c]]\n",
        "\"\"\"\n",
        "#Busco valores de c para que A sea diagonalizable\n",
        "c = Symbol('c')\n",
        "A = Matrix([[2, 0],\n",
        "            [2-c, c]])\n",
        "solve(chi(A), x) #las raices son dos: 2 y c\n",
        "#o(A) = {2, c} si c≠2    o   o(A) = {2 (doble)} si c=2\n",
        "#A es diagonalizable si tiene 2 autovalores diferentes: c≠2\n",
        "\n",
        "#CASO c≠2\n",
        "#Primer autovector: [1,1]\n",
        "#Segundo autovector:\n",
        "(A-c*eye(2,2)).nullspace()\n",
        "#Esos dos autovectores son una base de R2\n",
        "\n",
        "#CASO c=2\n",
        "A = A.subs(c,2) #A es diagonal\n",
        "#o(A) = {2 (doble)}\n",
        "(A-2*eye(2,2)).nullspace() #es todo R2\n",
        "#Cualquier base de R2 sirve como base de autovectores"
      ],
      "metadata": {
        "id": "fg8m96v1BSZB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "outputId": "de3dc453-81d9-4693-e452-8e1b772de1c5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\1\\end{matrix}\\right]\\right]$",
            "text/plain": [
              "⎡⎡1⎤  ⎡0⎤⎤\n",
              "⎢⎢ ⎥, ⎢ ⎥⎥\n",
              "⎣⎣0⎦  ⎣1⎦⎦"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Hallar, si existe, $A \\in \\mathbb R^{3 \\times 3}$ tal que $A^2 = \\begin{bmatrix}-2&-3&3\\\\3&4&-3\\\\-3&-3&4\\end{bmatrix}$."
      ],
      "metadata": {
        "id": "JAf2HMFGzUvn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#p = x^2, B = p(A) = A^2\n",
        "B = Matrix([[-2, -3,  3],\n",
        "            [3,   4, -3],\n",
        "            [-3, -3,  4]])\n",
        "#Obtengo o(B)\n",
        "pol = chi(B)\n",
        "raices = roots(pol) #{1(doble), 4}\n",
        "\n",
        "#Entonces o(A) ⊆ raiz(lambda de B) = {1, -1, 2, -2}\n",
        "\n",
        "#Calculo autoespacios asociados a cada autovalor de B:\n",
        "SB_1 = (B-eye(3,3)).nullspace() #autoespacio de B asociado a lambda = 1\n",
        "SB_4 = (B-4*eye(3,3)).nullspace() #autoespacio de B asociado a lambda = 4\n",
        "#Como las multiplicidades coinciden, B es diagonalizable -> B = P \\Lambda P^-1\n",
        "#P = [SB_1 SB_4], Lambda = diag(1,1,4)\n",
        "\n",
        "#Escribo o(A) eligiendo tres de las opciones: elijo o(A) = {1, 1, 2}\n",
        "#v ∈ nul(A-1.I) => v ∈ nul(B-p(1)I) => v ∈ nul(B-I)\n",
        "SA_1 = SB_1 #autovectores de A asocidados a lambda = 1\n",
        "#v ∈ nul(A-2.I) => v ∈ nul(B-p(2)I) => v ∈ nul(B-4I)\n",
        "SA_2 = SB_4 #autovectores de A asocidados a lambda = 2\n",
        "#Entonces:\n",
        "P = Matrix.hstack(*SA_1, *SA_2)\n",
        "Lambda = diag(1,1,2)\n",
        "A = P*Lambda*P.inv()"
      ],
      "metadata": {
        "id": "ZuKTkrip38Rh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Si juntamos dos poblaciones de bacterias $a$ y $b$, el comportamiento de las mismas se puede describir con las siguientes ecuaciones:\n",
        "\n",
        "$$\n",
        "\\begin{cases}\n",
        "a_n = \\frac{6}{5}\\, a_{n-1} - p\\; b_{n-1} \\\\\n",
        "b_n = \\frac{3}{5}\\, a_{n-1} + \\frac{2}{5}\\, b_{n-1}\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "**( a )** Hallar todos los valores de $p>0$ para los cuales la matriz del sistema resulta diagonalizable.\n",
        "\n",
        "**( b )** Para cada $p \\in \\left\\{ \\frac{1}{4}, \\frac{1}{5}, \\frac{77}{500}\\right\\}$ analizar el comportamiento a largo plazo de las dos especies."
      ],
      "metadata": {
        "id": "TBsC6OEKH8Sq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p, n, a0, b0 = symbols('p n a_0 b_0')\n",
        "A = Matrix([['6/5', -p],\n",
        "            ['3/5', '2/5']])\n",
        "\n",
        "#(a)\n",
        "\n",
        "raices = roots(chi(A),x)\n",
        "\n",
        "#CASO 1: Si 4-15p es mayor a 0: hay dos raices distintas\n",
        "#A es diagonalizable porque tiene dos autovalores distintos (y cada uno va a tener un autovector asociado)\n",
        "#p < 4/15\n",
        "\n",
        "#CASO 2: Si 4-15p es 0: hay una raíz doble\n",
        "#p = 4/15\n",
        "A2 = A.subs(p, Rational('4/15'))\n",
        "raices = roots(chi(A2),x)\n",
        "#Como hay un autovalor doble, tengo que checkear que el autoespacio asociado al autovalor tenga dim = 2\n",
        "(A2-Rational('4/5')*eye(2,2)).nullspace() #como dim = 1, en este caso A no es diagonalizable\n",
        "\n",
        "#Entonces A es diagonalizable si p ∈ (0, 4/15)\n",
        "\n",
        "#(b)\n",
        "A1 = A.subs(p, Rational('1/4'))\n",
        "A1.eigenvects()#A1 es diagonalizable\n",
        "DS(A1) #Como los autovalores son menores a 1, A1^k con k tendiendo a inf, tiende a 0\n",
        "limiteA1 = limite(A1)\n",
        "\n",
        "A2 = A.subs(p, Rational('1/5'))\n",
        "A2.eigenvects()#A2 es diagonalizable\n",
        "DS(A2) #A2^k con k tendiendo a inf, tiende al G correspondiente al autovalor 1: [[3/2, -1/2],[3/2, -1/2]]\n",
        "limiteA2 = limite(A2)\n",
        "v_init = Matrix([a0, b0])\n",
        "limiteA2 * v_init #Para que haya población, 3/2 a0 - 1/2 b0 > 0\n",
        "                    #                         b0 < 3a0                                              \n",
        "\n",
        "v_n = (A2**n * v_init)\n",
        "v_n = v_n.subs({\n",
        "    a0: 1,\n",
        "    b0: 2\n",
        "})\n",
        "p1 = plot(v_n[0],(n,0,100),show=False,line_color='blue',xlim=(0,7),ylim=(-4,4))\n",
        "p2 = plot(v_n[1],(n,0,100),show=False,line_color='orange',xlim=(0,7),ylim=(-4,4))\n",
        "p1.extend(p2)\n",
        "p1.show()\n",
        "\n",
        "A3 = A.subs(p, Rational('77/500'))\n",
        "A3.eigenvects()#A3 es diagonalizable\n",
        "DS(A3) #Como A2 tiene un autovalor mayor a 1, A2^k con k tendiendo a inf tiende a infinito\n",
        "limiteA3 = limite(A3)\n"
      ],
      "metadata": {
        "id": "gTWKZYOaIF48",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "766dcd54-1fbc-4840-d186-14eb98f9ba06"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FJKcwzNifGa5n2qXTI7yvP4c/zLLyoYE1c7l04s1o9pOy8mi0piUHty05uK8sKVn5sO2R2g3bHu3cQ7Yz3nc+5x5SU/5vORBQmBTKy6N5FmfGNMese/Ssb7ywy/b4+bQ9cya7EO6/wI5IXZ3U3n7+7xsSYMPCa7Rj5y6mRKIivcw4j/ddyLUGln5NSXRrSrJLFYmu6LUsWi9PROvlmYt1KTlsSahLyf4upT6Ypaq+XpWpV5axlHmXTCeibU/v99TZbXmvTKno2Nnt9HpsLPsQvX1XVmckoIAiMBvsaUwLdPakzAA9nzDs64t6qH19+Vn6+y/8valUdDs3n9c6dxxZmaSp6SU31dWjf4n/wrgSZX1KJnqVLOtVeSIVrae3k4mMfWWD+8uTqTG3M99XnuhVeTL9mkipPNmbsT+l8sTg9vD3DZz79tuz+zQEFABJUe9g6tRowaCB3m+hwtc9faey/9z1kfaNfdzU35+UezLH82S/r8el7vHe0yt5anBflvlEQAHAWDJ7vyiuUhlICwCYZAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQYg0oM7vNzPaY2Vtm9p/irAUAEJbYAsrMEpIek/RbkhZJusfMFsVVDwAgLHH2oFZIesvd33H3HklPSvpUjPUAAAIS5wTy8yS9n7HdJukjwxuZ2UZJGyWpvLxczc3NxamuSNrb21VXVxd3GXnFZyoNfKbSMBE/02uvvbbL3ZeM1y74Xzhx902SNknStGnTvKWlJeaK8qu5uVl8pvDxmUoDn6k0mFl3Nu3ivMW3T9L8jO2G9D4AAGINqJ9JutLMFphZhaR1kp6JsR4AQEBiu8Xn7r1m9keSfigpIelb7r57rPfMmjWrKLUV08aNG+MuIe/4TKWBz1QaJuJnUvqxzXjM3QtdSN40NzdPuGdQADAJWTaNmEkCABAkAgoAEKSSCKiBKZF27dqlr3zlK3GXkxf33Xef6uvrtWTJuF8FKBnvv/++Vq5cqUWLFmnx4sV69NFH4y4pZ93d3VqxYoWuvfZaLV68WI888kjcJeVNX1+fli5dqjVr1sRdSl40Njbq6quvVlNT04T5vmRHR4fuvvtuXXXVVVq4cKF+8pOfxF1STvbs2aOmpiaZ2c700mlmD47WPvhnUOkpkX4tadWyZcve7u3t1RNPPKFFi0p7VqStW7equrpan/3sZ7Vr1664y8mLAwcO6MCBA1q2bJlOnDih5cuX66mnnirpPyt316lTp1RdXa1UKqUbb7xRjz76qK6//vq4S8vZ1772NbW0tKizs1ObN2+Ou5ycNTY2qqWlZUINpvrc5z6nm266SRs2bFBPT49Onz6t2trauMvKB0v/3b5P0kfc/d2RGpVCD+rslEhmpnXr1unpp5+Ou6ac3XzzzZo5c2bcZeTVnDlztGzZMklSTU2NFi5cqH37SvurbWam6upqSVIqlVIqlZJZVs93g9bW1qZnn31WGzZsiLsUjOL48ePaunWr7r//fklSRUXFRAmnAZ+Q9PZo4SSVRkANmRKpoaGh5P/SmwxaW1v1+uuv6yMfOWf2qpLT19enpqYm1dfXa9WqVRPiMz344IP66le/qrKyUvgrIDtmptWrV2v58uXatCmrUcxB27t3r+rq6vT5z39eS5cu1YYNG3Tq1Km4y8qndZKeGKvBxPm/E8E4efKk1q5dq69//euaPn163OXkLJFIaOfOnWpra9P27dtL/pbs5s2bVV9fr+XLl8ddSl69+uqr2rFjh55//nk99thj2rp1a9wl5aS3t1c7duzQAw88oNdff13Tpk2bMM/g05Mz3CHp78dqVwoBNWRKpLa2Ns2bNy/GcjCWVCqltWvXav369brrrrviLievamtrtXLlSr3wwgtxl5KTbdu26ZlnnlFjY6PWrVunV155Rffee2/cZeVs4O+F+vp63Xnnndq+fXvMFeWmoaFBDQ0NZ3vsd999t3bs2BFzVXnzW5J2uPuhsRqVQkCdnRLJ3fXkk0/qjjvuiLsmjMDddf/992vhwoX6whe+EHc5edHe3q6Ojg5JUldXl7Zs2aKrrroq5qpy8+Uvf1ltbW1qbW3Vk08+qVtvvVWPP/543GXl5NSpUzpx4sTZ9RdffLHkR8jOnj1b8+fP1549eyRJL7/8ckkPOBrmHo1ze08qgYBy915JfyTph7t27dJnPvMZLV68OO6ycnbPPffohhtu0J49e9TQ0KBvfvObcZeUs23btunb3/62XnnlFTU1NampqUnPPfdc3GXl5MCBA1q5cqWuueYaXXfddVq1atWEGZY9kRw6dEg33nijrr32Wq1YsUK33367brvttrjLytk3vvENrV+/Xtdcc4127typhx56KO6ScpZ+jrZK0vfHaxv8MPNMTHUEABMCUx0BAEoXAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUAKIrW1lYtXLhQZvbXZrbbzF40s6rR2hNQAICiefPNNyXpMXdfLKlD0trR2hJQAICiWbBggdx9Z3rzNUmNo7UloAAARTNlypTMzT5JydHaxhJQZva76fuP/WbWHEcNAICwxdWD2iXpLkml/YtiAICCGbVrVUju/ksp+olmAMDk0NjYOOQXqd39z8dqH/wzKDPbaGYtZtbS3t4edzkAgCIpWA/KzF6SNHuEQw+7+9PZnsfdN0naJEW/B5Wn8gAAgStYQLn7Jwt1bgDAxBf8LT4AwOQU1zDzO82sTdINkp41sx/GUQcAIFxxjeL7gaQfxHFtAEBp4BYfACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEgEFAAgSAQUACBIBBQAIEixBJSZ/ZmZ/crMfm5mPzCz2jjqAACEK64e1BZJS9z9Gkm/lvSlmOoAAAQqloBy9xfdvTe9+a+SGuKoAwAQrhCeQd0n6fnRDprZRjNrMbOW9vb2IpYFAIiTuXthTmz2kqTZIxx62N2fTrd5WFKzpLs8i0Kam5u9paUlv4UCAIrNsmmULNTV3f2TYx03s9+XtEbSJ7IJJwDA5FKwgBqLmd0m6YuSPu7up+OoAQAQtrieQf1PSTWStpjZTjP7q5jqAAAEKpYelLtfEcd1AQClI4RRfAAAnIOAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABCmWgDKz/2pmPzeznWb2opnNjaMOAEC44upB/Zm7X+PuTZI2S/ovMdUBAAhULAHl7p0Zm9MkeRx1AADClYzrwmb23yR9VtJxSSvHaLdR0kZJuvTSS4tTHAAgduZemM6Lmb0kafYIhx5296cz2n1JUqW7PzLeOZubm72lpSWPVQIAYmDZNCpYD8rdP5ll0+9Iek7SuAEFAJg84hrFd2XG5qck/SqOOgAA4YrrGdRXzOzDkvolvSvpD2KqAwAQqFgCyt3XxnFdAEDpYCYJAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJAIKABAkAgoAECQCCgAQJBiDSgz+xMzczObFWcdAIDwxBZQZjZf0mpJ78VVAwAgXHH2oP5C0hcleYw1AAAClYzjomb2KUn73P3fzGy8thslbUxv7pa0pMDlAQACYO6F6cCY2UuSZo9w6GFJD0la7e7HzaxVUrO7HylIIQCAklSwgBr1gmZXS3pZ0un0rgZJ+yWtcPeDRS0GABCsogfUOQXQgwIAjIDvQQEAghR7DwoAgJHQgwIABImAAgAEiYACAASJgAIABImAAgAEiYACAASJgAIABOn/AyIrMWWQj0/bAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Sea $A\\in\\mathbb R^{3 \\times 3}$ la matriz dependiente del parámetro real $a$ definida por $\\begin{bmatrix}a^2&1&0\\\\0&(a+1)^2&0\\\\1&0&1\\end{bmatrix}$. Existe una matriz inversible $P\\in \\mathbb R^{3\\times 3}$ tal que $P^{-1}AP = \\begin{bmatrix}1&0&0\\\\0&\\frac14&1\\\\0&0&\\frac14\\end{bmatrix}$. Hallar el valor de $a$."
      ],
      "metadata": {
        "id": "k6fLLM6qdRB1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Como las matrices son semejantes, a^2= 1/4, y (a+1)^2 = 1/4, entonces a = -1/2."
      ],
      "metadata": {
        "id": "wrHIdEpieCfO"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Resolver el sistema $Y' = AY$, siendo $A = \\begin{bmatrix}\\dots\\end{bmatrix}$ "
      ],
      "metadata": {
        "id": "I_A7TvieZKzY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **($A$ diagonalizable)** Hallar un conjunto fundamental de soluciones del sistema $Y' = AY$, con condición inicial $Y(0) = Y_0$, siendo $A = \\begin{bmatrix}4&-3\\\\0&-2\\end{bmatrix}$.\n"
      ],
      "metadata": {
        "id": "vQHrS8SNIYki"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[4, -3],\n",
        "            [0, -2]])\n",
        "A.eigenvects() #tiene dos autovalores diferentes, es diagonalizable\n",
        "P, L = A.jordan_form() #entonces el conjunto fundamental de soluciones es: {e^(-2t)[1/2 1], e^(4t)[1 0]}\n",
        "#y(t) = a.e^(-2t)[1/2 1] + b.e^(4t)[1 0]\n",
        "#y(0) = a.[1/2 1] + b.[1 0] =  P . [a b]^T\n",
        "#P^(-1) y0 = [a b]^T\n",
        "n1, n2 = symbols('n_1, n_2')\n",
        "y0 = Matrix([n1, n2])\n",
        "a, b = P.inv()*y0\n",
        "#y(t) = a.e^(-2t)[1/2 1] + b.e^(4t)[1 0]\n",
        "A.eigenvects()"
      ],
      "metadata": {
        "id": "AvQNL6eUJPLb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "outputId": "cda3fa5e-1c4e-46f0-c9be-b657c121878a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left( -2, \\  1, \\  \\left[ \\left[\\begin{matrix}\\frac{1}{2}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 4, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]\\right]\\right)\\right]$",
            "text/plain": [
              "⎡⎛       ⎡⎡1/2⎤⎤⎞  ⎛      ⎡⎡1⎤⎤⎞⎤\n",
              "⎢⎜-2, 1, ⎢⎢   ⎥⎥⎟, ⎜4, 1, ⎢⎢ ⎥⎥⎟⎥\n",
              "⎣⎝       ⎣⎣ 1 ⎦⎦⎠  ⎝      ⎣⎣0⎦⎦⎠⎦"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **($A$ no diagonalizable, 2 autovalores)** Sea $Y$ la solución del problema de valores iniciales $Y' = \\begin{bmatrix}-1&0&0\\\\2&1&0\\\\-1&-1&1\\end{bmatrix}Y$, $Y(0) = \\begin{bmatrix}2\\\\1\\\\4\\end{bmatrix}$.\n",
        "\n",
        "Hallar $Y(ln(2))$."
      ],
      "metadata": {
        "id": "L0Vhso27ZjjO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[-1,0,0],\n",
        "            [2,1,0],\n",
        "            [-1,-1,1]])\n",
        "A.eigenvects() #no es diagonalizable\n",
        "P, L = A.jordan_form() #entonces el conjunto fundamental de soluciones es: {e^(t)[0 0 -1], e^(t)(t.[0 0 -1] + [0 1 0]), e^(-t)[-1 1 0]}\n",
        "P = Matrix.hstack(P.col(1), P.col(2), P.col(0))\n",
        "a, b, c, t = symbols('a,b,c,t')\n",
        "y = a*exp(t)*P.col(0) + b*exp(t)*(t*P.col(0) + P.col(1)) + c*exp(-t)*P.col(2)\n",
        "#y(0) = a.e^(t)[0 0 -1] + b.e^(t)(t.[0 0 -1] + [0 1 0]) + c.e^(-t)[-1 1 0] =  P . [a b c]^T\n",
        "#P^(-1) y0 = [a b c]^T\n",
        "y0 = Matrix([2, 1, 4])\n",
        "a_value, b_value, c_value = P.inv()*y0\n",
        "y = y.subs({a: a_value, b: b_value, c: c_value})\n",
        "y.subs({t: ln(2)})\n"
      ],
      "metadata": {
        "id": "ESGbl6JeW2J6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "outputId": "166a7ed3-4156-4bed-bd99-7aa8678cf2a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\\\5\\\\8 - 6 \\log{\\left(2 \\right)}\\end{matrix}\\right]$",
            "text/plain": [
              "⎡     1      ⎤\n",
              "⎢            ⎥\n",
              "⎢     5      ⎥\n",
              "⎢            ⎥\n",
              "⎣8 - 6⋅log(2)⎦"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[-1,1,1],\n",
        "            [0,1,1],\n",
        "            [0,0,1]])\n",
        "A.eigenvects() #no es diagonalizable\n",
        "P = Matrix([[-1,0,1],\n",
        "            [-2,1,0],\n",
        "            [0,-2,0]])\n",
        "Lambda = Matrix([[1,1,0],\n",
        "                 [0,1,0],\n",
        "                 [0,0,-1]])\n",
        "P*Lambda*P.inv()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "id": "0Z67oXIhQi1A",
        "outputId": "ac8cb5fa-1f14-4f20-87f5-c968f17daaba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1 & 1 & 1\\\\0 & 1 & 1\\\\0 & 0 & 1\\end{matrix}\\right]$",
            "text/plain": [
              "⎡-1  1  1⎤\n",
              "⎢        ⎥\n",
              "⎢0   1  1⎥\n",
              "⎢        ⎥\n",
              "⎣0   0  1⎦"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **($A$ no diagonalizable, 1 autovalor)** Resolver los sistemas $Y' = AY$ y $Y' = BY$, con $$A = \\begin{bmatrix}2&-1&1\\\\1&5&-2\\\\0&1&2\\end{bmatrix}\\quad y \\quad B = \\begin{bmatrix}1&2&-1\\\\0&2&0\\\\1&-2&3\\end{bmatrix}.$$\n"
      ],
      "metadata": {
        "id": "HRJFJmK4LgtC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[2, -1,  1],\n",
        "            [1,  5, -2],\n",
        "            [0,  1,  2]])\n",
        "A.eigenvects() #tiene un autovalor, m = 3, mu = 1, no es diagonalizable.\n",
        "N = A - 3*eye(3)\n",
        "N2 = N**2\n",
        "v = Matrix([0, 0, 1]) #v no pertenece al Nul(N2)\n",
        "P = Matrix.hstack(N2*v, N*v, v)\n",
        "L = Matrix([[3, 1, 0],\n",
        "            [0, 3, 1],\n",
        "            [0, 0, 3]])\n",
        "#Conj Fundamental de Soluciones = {e^(3t)N^2v, e^(3t)(tN^2v + Nv), e^(3t)(t^2/2 N^2v + Nvt + v)}\n",
        "\n",
        "B = Matrix([[1,  2, -1],\n",
        "            [0,  2,  0],\n",
        "            [1, -2,  3]])\n",
        "B.eigenvects() #tiene un autovalor, m = 3, mu = 2, no es diagonalizable.\n",
        "N = B - 2*eye(3)\n",
        "v1 = Matrix([-1, 2, -1]) #v no pertenece al Nul(N)\n",
        "N.nullspace(), N*v1\n",
        "v2 = Matrix([2, 1, 0]) #v pertenece al Nul(N), y es LI con N.v1\n",
        "P = Matrix.hstack(N*v1, v1, v2)\n",
        "L = Matrix([[2, 1, 0],\n",
        "            [0, 2, 0],\n",
        "            [0, 0, 2]])\n",
        "#Conj Fundamental de Soluciones = {e^(2t)Nv1, e^(2t)(tNv1 + v1), e^(2t)v2}"
      ],
      "metadata": {
        "id": "tKQR0PmqMJjb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **($A$ no diagonalizable, autovalores complejos)** Resolver el sistema $Y' = AY$, con $$A = \\begin{bmatrix}4&0&0\\\\0&60&18\\\\0&-50&60\\end{bmatrix}.$$\n"
      ],
      "metadata": {
        "id": "oauDikRuWpJb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[4,   0,  0],\n",
        "            [0,  60, 18],\n",
        "            [0, -50, 60]])\n",
        "A.eigenvects() #tiene autovalores imaginarios, no es diagonalizable\n",
        "#Autovalores: 4,         asociado al [1   0 0]\n",
        "#             60 - 30 i, asociado al [0  3i 5]\n",
        "#             60 + 30 i, asociado al [0 -3i 5]\n",
        "\n",
        "#Del autovalor imaginario 60 + 30 i, descompongo el autovector: [0 -3i 5] = [0 0 5] + i.[0 -3 0] = x + iy.\n",
        "#Conjunto Fundamental de soluciones: {e^(60t)cos(30t)[0 0 5] - e^(60t)sen(30t)[0 -3 0], e^(60t)sen(30t)[0 0 5] + e^(60t)cos(30t)[0 -3 0]}\n",
        "\n",
        "#Del autovalor 4: {e^(4t)[1 0 0]}\n",
        "\n",
        "#Junto todo: Conjunto fundamental de soluciones = {e^(4t)[1 0 0], e^(60t)cos(30t)[0 0 5] - e^(60t)sen(30t)[0 -3 0], e^(60t)sen(30t)[0 0 5] + e^(60t)cos(30t)[0 -3 0]"
      ],
      "metadata": {
        "id": "HgtLUM4HW9x6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "outputId": "413a2c66-fb43-4074-ba38-9014c00ddddf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left( 4, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\0\\\\0\\end{matrix}\\right]\\right]\\right), \\  \\left( 60 - 30 i, \\  1, \\  \\left[ \\left[\\begin{matrix}0\\\\\\frac{3 i}{5}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 60 + 30 i, \\  1, \\  \\left[ \\left[\\begin{matrix}0\\\\- \\frac{3 i}{5}\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$",
            "text/plain": [
              "⎡               ⎛              ⎡⎡ 0 ⎤⎤⎞  ⎛              ⎡⎡  0  ⎤⎤⎞⎤\n",
              "⎢⎛      ⎡⎡1⎤⎤⎞  ⎜              ⎢⎢   ⎥⎥⎟  ⎜              ⎢⎢     ⎥⎥⎟⎥\n",
              "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜              ⎢⎢3⋅ⅈ⎥⎥⎟  ⎜              ⎢⎢-3⋅ⅈ ⎥⎥⎟⎥\n",
              "⎢⎜4, 1, ⎢⎢0⎥⎥⎟, ⎜60 - 30⋅ⅈ, 1, ⎢⎢───⎥⎥⎟, ⎜60 + 30⋅ⅈ, 1, ⎢⎢─────⎥⎥⎟⎥\n",
              "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜              ⎢⎢ 5 ⎥⎥⎟  ⎜              ⎢⎢  5  ⎥⎥⎟⎥\n",
              "⎢⎝      ⎣⎣0⎦⎦⎠  ⎜              ⎢⎢   ⎥⎥⎟  ⎜              ⎢⎢     ⎥⎥⎟⎥\n",
              "⎣               ⎝              ⎣⎣ 1 ⎦⎦⎠  ⎝              ⎣⎣  1  ⎦⎦⎠⎦"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Resolver el sistema $Ax' = x$ con $A = \\begin{bmatrix}-5&-1&1\\\\0&9&-7\\\\0&14&-12\\end{bmatrix}$ y hallar los posibles valores de $x(0)$ para los cuales $\\lim_{t→∞} \\|x(t)\\| = 0$."
      ],
      "metadata": {
        "id": "WyFbCZ1jTn8Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Matrix([[-5, -1,   1],\n",
        "            [ 0,  9,  -7],\n",
        "            [ 0, 14, -12]])\n",
        "A.eigenvects() #tiene dos autovalores,-5 y 2, m(-5) = 2, mu(-5) = 1 -> A no es diagonalizable.\n",
        "N1 = A + 5*eye(3)\n",
        "N2 = A - 2*eye(3)\n",
        "N12 = N1**2\n",
        "N12.nullspace(), N1.nullspace()\n",
        "v1 = Matrix([0, 1, 2]) #v1 pertenece al Nul(N1^2), y no pertenece al Nul(N1)\n",
        "N2.nullspace()\n",
        "v2 = Matrix([0, 1, 1]) #v2 pertenece al Nul(N2)\n",
        "P = Matrix.hstack(N1*v1, v1, v2)\n",
        "L = Matrix([[-5,  1, 0],\n",
        "            [ 0, -5, 0],\n",
        "            [ 0,  0, 2]])\n",
        "#Conj Fundamental de Soluciones = {e^(-5t)N1v1, e^(-5t)(tN1v1 + v1), e^(2t)v2}\n",
        "#x = a.e^(-5t)N1v1 + b.e^(-5t)(tN1v1 + v1) + c.e^(2t)v2\n",
        "#Si tienda a inf: x = c.e^(GRANDE)v2 = 0 => no queda otra a que c = 0.\n"
      ],
      "metadata": {
        "id": "gdt7x58MUJDR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Ejercicios Stop**"
      ],
      "metadata": {
        "id": "wi4rMctuGMO2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**2.** Sea $A \\in \\mathbb R^{3 \\times 3}$ que tiene autovalores $\\lambda_1 = 0, \\lambda_2 = 2, \\lambda_3 = 5$, con autovectores asociados $v_1 = \\begin{bmatrix}1&1&-1\\end{bmatrix}^T, \\begin{bmatrix}2&2&-1\\end{bmatrix}^T, \\begin{bmatrix}1&2&-1\\end{bmatrix}^T$ respectivamente.\n",
        "\n",
        "**(a)** Hallar una base de $nul(A)$ y una base de $col(A)$.\n",
        "\n",
        "**(b)** Hallar una solución particular de la ecuación $Ax = v_2 + v_3$.\n",
        "\n",
        "**(c)** Hallar todas las soluciones de la ecuación $Ax = v_2 + v_3$.\n",
        "\n",
        "\n",
        "**(d)** Explicar por qué la ecuación $Ax = v_1$ no tiene solución."
      ],
      "metadata": {
        "id": "7svx10juZx1W"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#(a)\n",
        "#Analizo:\n",
        "#A.v1 = 0.v1 -> Nul(A)\n",
        "#Como dim(Nul(A)) = 1, entonces como n - dim(Nul(A)) = dim(Col(A)) -> dim(Col(A)) = 2 \n",
        "#A.v2 = 2.v2 -> Col(A) \n",
        "#A.v3 = 5.v3 -> Col(A)\n",
        "\n",
        "#Entonces: Nul(A) = {v1}, Col(A) = {v2, v3}\n",
        "\n",
        "#(b)\n",
        "#Tomo Base B = {v1, v2, v3}\n",
        "v1 = Matrix([1, 0, 0])\n",
        "v2 = Matrix([0, 1, 0])\n",
        "v3 = Matrix([0, 0, 1])\n",
        "\n",
        "B = [v1,v2,v3]\n",
        "W = [0*v1, 2*v2, 5*v3]\n",
        "b = v2 + v3\n",
        "sol, sp, gen = gauss_jordan_con_generadores(Matrix.hstack(*W), b)\n",
        "#A(sp) = b\n",
        "\n",
        "#(c)\n",
        "#sol general = sp + gen(gen), es decir, sg = sp + gen(Nu(A))\n",
        "\n",
        "#(d)\n",
        "#Porque v1 no pertenece a Col(A)\n"
      ],
      "metadata": {
        "id": "WlTr022Na5O_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**4.** Sea $A\\in\\mathbb R^{3\\times 3}$ la matriz dependiente de los parametros $a,b,c \\in \\mathbb R / A = \\begin{bmatrix}0&1&0\\\\0&0&1\\\\c&b&a\\end{bmatrix}$.\n",
        "\n",
        "**(a)** Hallar los valores de $a,b,c \\in \\mathbb R$ tales que $\\chi_A(x) = det(A-xI) = 9x - x^3$. ¿$A$ es diagonalizable?\n",
        "\n",
        "**(b)** Para $c = 0$, hallar el conjunto de todas las parejas $a,b$ tales que $A$ es diagonalizable."
      ],
      "metadata": {
        "id": "cIHlmXtTom6g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a,b,c,x = symbols('a,b,c,x')\n",
        "A = Matrix([[0, 1,0],\n",
        "            [0, 0,1],\n",
        "            [c,b,a]])\n",
        "\n",
        "#Busco valores de c para que A sea diagonalizable\n",
        "(A-x*eye(3,3)).det() #como tiene que ser igual a 9x - x^3 => a = c = 0, b = 9\n",
        "A1 = A.subs({a:0, c:0, b:9})\n",
        "\n",
        "solve(chi(A1), x) #las raices son dos: -3, 0, 3\n",
        "A1.diagonalize()\n",
        "\n",
        "#(b): tengo q ver q pasa cuando los autovalores son dobles (q esos generen autoespacio doble)"
      ],
      "metadata": {
        "id": "7nP41dQgpchn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "outputId": "02f84363-dea6-4745-b451-8ac4cdfd0605"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 1 & 1\\\\-3 & 0 & 3\\\\9 & 0 & 9\\end{matrix}\\right], \\  \\left[\\begin{matrix}-3 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 3\\end{matrix}\\right]\\right)$",
            "text/plain": [
              "⎛⎡1   1  1⎤  ⎡-3  0  0⎤⎞\n",
              "⎜⎢        ⎥  ⎢        ⎥⎟\n",
              "⎜⎢-3  0  3⎥, ⎢0   0  0⎥⎟\n",
              "⎜⎢        ⎥  ⎢        ⎥⎟\n",
              "⎝⎣9   0  9⎦  ⎣0   0  3⎦⎠"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**6.** Hallar, si existe, $A \\in \\mathbb R^{2 \\times 2}$ tal que:\n",
        "\n",
        "**(a)** $A^2 - 3A + 2I = \\begin{bmatrix}3&3\\\\3&3\\end{bmatrix}$.\n",
        "\n",
        "**(b)** $A^2 - 3A + 2I = \\begin{bmatrix}3&3\\\\3&3\\end{bmatrix}$ y $det(A) = -1$.\n",
        "\n",
        "**(c)** $A^2 - 3A + 2I = \\begin{bmatrix}3&3\\\\3&3\\end{bmatrix}$ y $tr(A) = 6$."
      ],
      "metadata": {
        "id": "ukepBWo0Bqx1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#p = x^2-3x+2, B = p(A) = A^2-3A+2\n",
        "B = Matrix([[3,  3],\n",
        "            [3,  3]])\n",
        "\n",
        "#(a)\n",
        "\n",
        "#Obtengo o(B)\n",
        "pol = chi(B)\n",
        "raices = roots(pol) #{0, 6}\n",
        "\n",
        "#Entonces o(A) ⊆ {2, 1, 4, -1}\n",
        "\n",
        "#Calculo autoespacios asociados a cada autovalor de B:\n",
        "SB_1 = (B-0*eye(2,2)).nullspace() #autoespacio de B asociado a lambda = 0\n",
        "SB_2 = (B-6*eye(2,2)).nullspace() #autoespacio de B asociado a lambda = 6\n",
        "#Como las multiplicidades coinciden, B es diagonalizable -> B = P \\Lambda P^-1\n",
        "#P = [SB_1 SB_2], Lambda = diag(0,6)\n",
        "\n",
        "#Escribo o(A) eligiendo tres de las opciones: elijo o(A) = {2, 4}\n",
        "#v ∈ nul(A-2.I) => v ∈ nul(B-p(2)I) => v ∈ nul(B-0I)\n",
        "SA_1 = SB_1 #autovectores de A asocidados a lambda = 2\n",
        "#v ∈ nul(A-4.I) => v ∈ nul(B-p(4)I) => v ∈ nul(B-6I)\n",
        "SA_2 = SB_2 #autovectores de A asocidados a lambda = 4\n",
        "#Entonces:\n",
        "P = Matrix.hstack(*SA_1, *SA_2)\n",
        "Lambda = diag(2, 4)\n",
        "A = P*Lambda*P.inv()\n",
        "A**2 - 3*A + 2*eye(2) #checkeo\n",
        "\n",
        "#(b)\n",
        "#Elijo o(A) tal que lambda1 * lambda2 = -1 => lambda1 = 1, lambda2 = -1\n",
        "#o(A) = {1, -1}\n",
        "SA_1 = SB_1 #autovectores de A asocidados a lambda = 1\n",
        "SA_2 = SB_2 #autovectores de A asocidados a lambda = -1\n",
        "#Entonces:\n",
        "P = Matrix.hstack(*SA_1, *SA_2)\n",
        "Lambda = diag(1, -1)\n",
        "A = P*Lambda*P.inv()\n",
        "A**2 - 3*A + 2*eye(2) #checkeo\n",
        "\n",
        "#(c)\n",
        "#Elijo o(A) tal que lambda1 + lambda2 = 6 => lambda1 = 2, lambda2 = 4\n",
        "#o(A) = {1, -1}\n",
        "SA_1 = SB_1 #autovectores de A asocidados a lambda = 2\n",
        "SA_2 = SB_2 #autovectores de A asocidados a lambda = 4\n",
        "#Entonces:\n",
        "P = Matrix.hstack(*SA_1, *SA_2)\n",
        "Lambda = diag(2, 4)\n",
        "A = P*Lambda*P.inv()\n",
        "A**2 - 3*A + 2*eye(2) #checkeo"
      ],
      "metadata": {
        "id": "W00KMfNTCB3-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "outputId": "1e06691a-4ae9-4326-f59a-537aff231a6b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}3 & 3\\\\3 & 3\\end{matrix}\\right]$",
            "text/plain": [
              "⎡3  3⎤\n",
              "⎢    ⎥\n",
              "⎣3  3⎦"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**7.** Si juntamos dos especies, una especie hervíbora $x$ y una especie carnívora $y$, la evolución de las mismas se puede describir con las siguientes ecuaciones:\n",
        "\n",
        "$$\n",
        "\\begin{cases}\n",
        "x_{n+1} = (1 + \\frac{2}{10}) x_n - py_n. \\\\\n",
        "y_{n+1} = \\frac{1}{2} x_n + (1 - \\frac{4}{10}) y_n.\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "**( a )** Hallar todos los valores de $p$ para los cuales la matriz del sistema resulta diagonalizable.\n",
        "\n",
        "**( b )** Para cada $p \\in \\left\\{ \\frac{7}{40}, \\frac{4}{25}, \\frac{1}{10}\\right\\}$ analizar la evolución de las dos especies."
      ],
      "metadata": {
        "id": "JZqpT5D8DUTV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p, n, a0, b0 = symbols('p n a_0 b_0')\n",
        "A = Matrix([[Rational('6/5'), -p],\n",
        "            [Rational('1/2'), Rational('3/5')]])\n",
        "\n",
        "#(a)\n",
        "\n",
        "raices1 = roots(chi(A),x)\n",
        "\n",
        "#CASO 1: Si 9-50p es mayor a 0: hay dos raices distintas\n",
        "#A es diagonalizable porque tiene dos autovalores distintos (y cada uno va a tener un autovector asociado)\n",
        "#p < 9/50\n",
        "\n",
        "#CASO 2: Si 9/50 es 0: hay una raíz doble\n",
        "#p = 9/50\n",
        "A2 = A.subs(p, Rational('9/50'))\n",
        "raices = roots(chi(A2),x)#lambda = 9/10\n",
        "#Como hay un autovalor doble, tengo que checkear que el autoespacio asociado al autovalor tenga dim = 2\n",
        "(A2-Rational('9/10')*eye(2,2)).nullspace() #como dim = 1, en este caso A no es diagonalizable\n",
        "\n",
        "#Entonces A es diagonalizable si p ∈ (0, 9/50)\n",
        "\"\"\"\n",
        "#(b)\n",
        "A1 = A.subs(p, Rational('7/40'))\n",
        "A1.eigenvects()#A1 es diagonalizable\n",
        "DS(A1) #Como los autovalores son menores a 1, A1^k con k tendiendo a inf, tiende a 0\n",
        "limite(A1)\n",
        "\n",
        "\n",
        "A2 = A.subs(p, Rational('4/25'))\n",
        "A2.eigenvects()#A2 es diagonalizable\n",
        "DS(A2) #A2^k con k tendiendo a inf, tiende al G correspondiente al autovalor 1: [[2, -4/5],[5/2, -1]]\n",
        "v_init = Matrix([a0, b0])\n",
        "limite(A2) * v_init #Para que haya población, 2 a0 - 4/5 b0 > 0         y     5/2 a0 - b0 > 0 \n",
        "                    #                                  2 a0 > 4/5 b0               5/2 a0 > b0\n",
        "                    #                                    a0 > 2/5 b0                   a0 > 2/5 b0\n",
        "                    #                                                       \n",
        "\n",
        "v_n = (A2**n * v_init)\n",
        "v_n = v_n.subs({\n",
        "    a0: Rational('3/5'),\n",
        "    b0: 1\n",
        "})\n",
        "p1 = plot(v_n[0],(n,0,100),show=False,line_color='blue',xlim=(0,20),ylim=(-1.5,1.5))\n",
        "p2 = plot(v_n[1],(n,0,100),show=False,line_color='orange',xlim=(0,20),ylim=(-1.5,1.5))\n",
        "p1.extend(p2)\n",
        "p1.show()\n",
        "\n",
        "\n",
        "A3 = A.subs(p, Rational('1/10'))\n",
        "A3.eigenvects()#A3 es diagonalizable\n",
        "DS(A3) #Como A2 tiene un autovalor mayor a 1, A2^k con k tendiendo a inf tiende a infinito\n",
        "limite(A3)\n",
        "\"\"\"\n",
        "A1 = A.subs(p, Rational('7/40'))\n",
        "P, a = A1.diagonalize()#A1 es diagonalizable\n",
        "P, DS(A1)"
      ],
      "metadata": {
        "id": "WPvehTCQE0SV",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 58
        },
        "outputId": "599cbe19-befe-428a-b9c0-cdc6e1b173b4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 7\\\\2 & 10\\end{matrix}\\right], \\  \\left[ \\frac{17}{20}, \\  \\left[\\begin{matrix}- \\frac{5}{2} & \\frac{7}{4}\\\\-5 & \\frac{7}{2}\\end{matrix}\\right], \\  \\frac{19}{20}, \\  \\left[\\begin{matrix}\\frac{7}{2} & - \\frac{7}{4}\\\\5 & - \\frac{5}{2}\\end{matrix}\\right]\\right]\\right)$",
            "text/plain": [
              "⎛⎡1  7 ⎤  ⎡17  ⎡-5/2  7/4⎤  19  ⎡7/2  -7/4⎤⎤⎞\n",
              "⎜⎢     ⎥, ⎢──, ⎢         ⎥, ──, ⎢         ⎥⎥⎟\n",
              "⎝⎣2  10⎦  ⎣20  ⎣ -5   7/2⎦  20  ⎣ 5   -5/2⎦⎦⎠"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**8.** Sea $A\\in\\mathbb R^{3 \\times 3}$ definida por $$A = \\begin{bmatrix}0.7&0.2&0.1\\\\0.3&0.5&0.2\\\\0.2&0.4&0.4\\end{bmatrix}$$\n",
        "\n",
        "**(a)** Hallar el espectro de $A$ y comprobar que $A$ es diagonalizable\n",
        "\n",
        "**(b)** Calcular $\\lim_{n\\rightarrow \\infty}A^n$ (en realidad piden otra cosa pero lo hago en papel)"
      ],
      "metadata": {
        "id": "Kfyyn86HXLNW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Rational('1/10')*Matrix([[7, 2, 1],\n",
        "                             [3, 5, 2],\n",
        "                             [2, 4, 4]])\n",
        "A.eigenvects() #3 autovalores, entonces A es diagonalizable\n",
        "#DS(A), limite(A) #Como un autovalor es 1, y el resto menores a 1, tiende a G1\n",
        "#lo comento porque sino se me tilda"
      ],
      "metadata": {
        "id": "JwTaKZX5Xpii",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "outputId": "fe7da0b7-531c-4db4-fdb3-b132f44ab47c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/latex": "$\\displaystyle \\left[ \\left( 1, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\frac{3}{10} - \\frac{\\sqrt{2}}{10}, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{-3 + \\sqrt{2}}{14 + 14 \\sqrt{2}}\\\\- \\frac{2 \\sqrt{2} + 5}{4 + 6 \\sqrt{2}}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\frac{\\sqrt{2}}{10} + \\frac{3}{10}, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{\\sqrt{2} + 3}{-14 + 14 \\sqrt{2}}\\\\- \\frac{-5 + 2 \\sqrt{2}}{-4 + 6 \\sqrt{2}}\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$",
            "text/plain": [
              "⎡               ⎛            ⎡⎡-(-3 + √2)  ⎤⎤⎞  ⎛            ⎡⎡  -(√2 + 3)  ⎤⎤\n",
              "⎢               ⎜            ⎢⎢─────────── ⎥⎥⎟  ⎜            ⎢⎢ ─────────── ⎥⎥\n",
              "⎢⎛      ⎡⎡1⎤⎤⎞  ⎜            ⎢⎢ 14 + 14⋅√2 ⎥⎥⎟  ⎜            ⎢⎢ -14 + 14⋅√2 ⎥⎥\n",
              "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜3    √2     ⎢⎢            ⎥⎥⎟  ⎜√2   3      ⎢⎢             ⎥⎥\n",
              "⎢⎜1, 1, ⎢⎢1⎥⎥⎟, ⎜── - ──, 1, ⎢⎢-(2⋅√2 + 5) ⎥⎥⎟, ⎜── + ──, 1, ⎢⎢-(-5 + 2⋅√2) ⎥⎥\n",
              "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜10   10     ⎢⎢────────────⎥⎥⎟  ⎜10   10     ⎢⎢─────────────⎥⎥\n",
              "⎢⎝      ⎣⎣1⎦⎦⎠  ⎜            ⎢⎢  4 + 6⋅√2  ⎥⎥⎟  ⎜            ⎢⎢  -4 + 6⋅√2  ⎥⎥\n",
              "⎢               ⎜            ⎢⎢            ⎥⎥⎟  ⎜            ⎢⎢             ⎥⎥\n",
              "⎣               ⎝            ⎣⎣     1      ⎦⎦⎠  ⎝            ⎣⎣      1      ⎦⎦\n",
              "\n",
              "⎞⎤\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎟⎥\n",
              "⎠⎦"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**13.** Para cada una de las siguientes matrices $A\\in \\mathbb R^{2\\times 2}$, hallar un conjunto fundamental de soluciones del sistema $Y0 = AY$, resolver el problema de valores iniciales $Y' = AY, Y(0) = Y_0$ y analizar su comportamiento asintótico:\n",
        "\n",
        "**(a)** $ \\quad A = \\begin{bmatrix}-1&-2\\\\0&-3\\end{bmatrix},\\quad$ **(b)** $\\quad A = \\begin{bmatrix}1&-2\\\\0&-3\\end{bmatrix}, \\quad$ **(c)** $\\quad A = \\begin{bmatrix}1&-2\\\\0&3\\end{bmatrix}$ "
      ],
      "metadata": {
        "id": "XA712-qQ9TP9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#(a)\n",
        "A = Matrix([[-1, -2],\n",
        "            [0, -3]])\n",
        "A.eigenvects() #tiene dos autovalores diferentes, es diagonalizable\n",
        "P, L = A.jordan_form() #entonces el conjunto fundamental de soluciones es: {e^(-3t)[1 1], e^(-1t)[1 0]}\n",
        "#y(t) = a.e^(-3t)[1 1] + b.e^(-1t)[1 0]\n",
        "#y(0) = a.[1 1] + b.[1 0] =  P . [a b]^T\n",
        "#P^(-1) y0 = [a b]^T\n",
        "n1, n2 = symbols('n_1, n_2')\n",
        "y0 = Matrix([n1, n2])\n",
        "a, b = P.inv()*y0\n",
        "#y(t) = n2.e^(-3t)[1 2] + (n1 - n2).e^(-t)[1 0]\n",
        "#lim y(inf) = 0 + 0 -> tiende a 0\n",
        "\n",
        "#(b)\n",
        "A = Matrix([[1, -2],\n",
        "            [0, -3]])\n",
        "A.eigenvects() #tiene dos autovalores diferentes, es diagonalizable\n",
        "P, L = A.jordan_form() #entonces el conjunto fundamental de soluciones es: {e^(-3t)[1 2], e^(1t)[1 0]}\n",
        "#y(t) = a.e^(-3t)[1 2] + b.e^(t)[1 0]\n",
        "#y(0) = a.[1 2] + b.[1 0] =  P . [a b]^T\n",
        "#P^(-1) y0 = [a b]^T\n",
        "n1, n2 = symbols('n_1, n_2')\n",
        "y0 = Matrix([n1, n2])\n",
        "a, b = P.inv()*y0\n",
        "#y(t) = n2.e^(-3t)[1 2] + (n1 - n2/2).e^(t)[1 0]\n",
        "#lim y(inf) = 0 + (n1 - n2/2).inf -> si n1-n2/2 =/= 0 => tiende a infinito;\n",
        "#                                    si n1-n2/2  =  0 => tiende a 0.\n",
        "\n",
        "#(c)\n",
        "A = Matrix([[1, -2],\n",
        "            [0,  3]])\n",
        "A.eigenvects() #tiene dos autovalores diferentes, es diagonalizable\n",
        "P, L = A.jordan_form() #entonces el conjunto fundamental de soluciones es: {e^(t)[1 0], e^(3t)[-1 1]}\n",
        "#y(t) = a.e^(t)[1 0] + b.e^(3t)[-1 1]\n",
        "#y(0) = a.[1 0] + b.[-1 1] =  P . [a b]^T\n",
        "#P^(-1) y0 = [a b]^T\n",
        "n1, n2 = symbols('n_1, n_2')\n",
        "y0 = Matrix([n1, n2])\n",
        "a, b = P.inv()*y0\n",
        "#y(t) = (n1+n2).e^(t)[1 0] + n2.e^(3t)[-1 1]\n",
        "#lim y(inf) = (n1+n2).inf + n2.inf -> si n1 + n2 =/= 0 => tiende a infinito;\n",
        "#                                     si n2 =/= 0 => tiende a infinito;\n",
        "#                                     si n1 + n2 = 0 y n2 = 0 => tiende a 0."
      ],
      "metadata": {
        "id": "-PBhGdoNGcJ0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**16.** Sea $A \\in \\mathbb R^{3 \\times 3}$ la matriz definida por $$A = \\frac{1}{18} \\begin{bmatrix}25&-14&-4\\\\-2&4&14\\\\-10&2&25\\end{bmatrix}$$\n",
        "\n",
        "**(a)** Hallar un conjunto fundamental de soluciones del sistema $Y'= AY$.\n",
        "\n",
        "**(b)** Resolver el problema de valores iniciales $Y' = AY$, $Y(0)=Y_0$ y analizar su comportamiento asintótico."
      ],
      "metadata": {
        "id": "EFopokvwRYex"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = Rational('1/18') * Matrix([[25, -14, -4],\n",
        "                               [-2,   4, 14],\n",
        "                               [-10,  2, 25]])\n",
        "A.eigenvects() #tiene un autovalor con m = 2, mu = 1\n",
        "N1 = A - eye(3)/2\n",
        "N12 = N1**2\n",
        "N2 = A - 2*eye(3)\n",
        "N12.nullspace(), N1.nullspace()\n",
        "v1 = Matrix([1, 2, 0]) #v pertenece a nul(N1^2) pero no a nul(N1) \n",
        "N2.nullspace()\n",
        "v2 = Matrix([-2, 1, 2]) #v pertenece a nul(N2) \n",
        "P = Matrix.hstack(N1*v1, v1, v2)\n",
        "L = Matrix([[Rational('1/2'), 1, 0],\n",
        "            [0, Rational('1/2'), 0],\n",
        "            [0, 0, 2]])\n",
        "#entonces el conjunto fundamental de soluciones es: {e^(t/2)[-2/3 -2/3 -1/3], e^(t/2)(t.[-2/3 -2/3 -1/3] + [1 2 0]), e^(2t)[-2 1 2]}\n",
        "#y(t) = a.e^(t/2)[-2/3 -2/3 -1/3] + b.e^(t/2)(t.[-2/3 -2/3 -1/3] + [1 2 0]) + c.e^(2t)[-2 1 2]\n",
        "#y(0) = a.[-2/3 -2/3 -1/3] + b.[1 2 0] + c[-2 1 2] =  P . [a b c]^T\n",
        "#P^(-1) y0 = [a b c]^T\n",
        "n1, n2, n3 = symbols('n_1, n_2, n_3')\n",
        "y0 = Matrix([n1, n2, n3])\n",
        "a, b, c = P.inv()*y0\n",
        "#y(t) = a.e^(t/2)[-2/3 -2/3 -1/3] + b.e^(t/2)(t.[-2/3 -2/3 -1/3] + [1 2 0]) + c.e^(2t)[-2 1 2]\n",
        "#lim y(inf) = inf + inf + inf -> se acota solo si a = b = c = 0."
      ],
      "metadata": {
        "id": "YIjEL7I0STDZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 4.**18.** Hallar todas las soluciones $Y \\in C^\\infty(\\mathbb R, \\mathbb R^3)$ del sistema $$Y' = \\begin{bmatrix}1&4&3\\\\3&-2&7\\\\7&-4&5\\end{bmatrix}Y$$ y determinar para qué valores iniciales $Y(0)\\in \\mathbb R^3$ la norma de $Y(t)$ es acotada para $t → ∞$"
      ],
      "metadata": {
        "id": "FG8IZDQrZM1K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A =  Matrix([[ 1,  4,  3],\n",
        "             [ 3, -2,  7],\n",
        "             [ 7, -4,  5]])\n",
        "A.eigenvects() #tiene autovalores imaginarios, no es diagonalizable\n",
        "#Autovalores: 8,        asociado al [1   1 1]\n",
        "#             -2 - 4 i, asociado al [-1  i 1]\n",
        "#             -2 + 4 i, asociado al [-1 -i 1]\n",
        "\n",
        "#Del autovalor imaginario -2 + 4 i, descompongo el autovector: [-1  i 1] = [-1 0 1] + i.[0 -1 0] = x + iy.\n",
        "x, y = Matrix([-1, 0, 1]), Matrix([0, -1, 0])\n",
        "P = Matrix.hstack(Matrix([1, 1, 1]), x, y)\n",
        "#a = -2, b = 4\n",
        "#Conjunto Fundamental de soluciones: {e^(-2t)cos(4t)[-1 0 1] - e^(-2t)sen(4t)[0 -1 0], e^(-2t)sen(4t)[-1 0 1] + e^(-2t)cos(4t)[0 -1 0]}\n",
        "\n",
        "#Del autovalor 8: {e^(8t)[1 1 1]}\n",
        "\n",
        "#Junto todo: Conjunto fundamental de soluciones = {e^(8t)[1 1 1], e^(-2t)cos(4t)[-1 0 1] - e^(-2t)sen(4t)[0 -1 0], e^(-2t)sen(4t)[-1 0 1] + e^(-2t)cos(4t)[0 -1 0]}\n",
        "#y(t) = a.e^(8t)[1 1 1] + b.(e^(-2t)cos(4t)[-1 0 1] - e^(-2t)sen(4t)[0 -1 0]) + c.(e^(-2t)sen(4t)[-1 0 1] + e^(-2t)cos(4t)[0 -1 0])\n",
        "#y(0) = a.[1 1 1] + b.[-1 0 1] + c.[0 1 0] =  P . [a b c]^T\n",
        "#P^(-1) y0 = [a b c]^T\n",
        "n1, n2, n3 = symbols('n_1, n_2, n_3')\n",
        "y0 = Matrix([n1, n2, n3])\n",
        "a, b, c = P.inv()*y0\n",
        "\n",
        "#y(inf) = inf + 0 + 0\n",
        "#Para a=0 el lim es acotado.\n",
        "solve(a)"
      ],
      "metadata": {
        "id": "8vL5HzbwaNQD",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 38
        },
        "outputId": "a6ba45df-b00d-4c29-a407-f0f0818668f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "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\n",
            "text/latex": "$\\displaystyle \\left[ \\left\\{ n_{1} : - n_{3}\\right\\}\\right]$",
            "text/plain": [
              "[{n₁: -n₃}]"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ]
    }
  ]
}