This repository contains an implementation of Row-Echelon form, Reduced Row-Echelon form and Matrix inversion using the Gauss algorithm and corresponding visualizations.
The file Matrix.py contains a base class for matrices allowing row operations named Matrix and a class SimpleMatrix which implements these operations based on arrays.
The file RowEchelon.py is responsible for converting a Matrix to Row-Echelon form using a function to_row_echelon_form() using row transformations.
A matrix is in Row-Echelon form if
- The leading coefficient of each non-zero row is strictly to the right of the leading coefficients of previous row.
- All zero-only rows are at the bottom of the matrix
If a parameter reduced is set to True, the Matrix is instead converted to Reduced Row-Echelon form.
A matrix is in Reduced Row-Echelon form if
- It is in Row-Echelon form.
- All leading coefficients are
1. - In every column that contains a leading
1, all other numbers are0.
The file FindInverse.py is responsible for calculating the inverse of a matrix using the function get_inverse().
The inverse of a matrix is the matrix that, multiplied with the original matrix, yields the identity matrix.
The file visualization.py provides a visualization of the algorithms using TKinter.
For this, it uses a custom Matrix implementation named VisualizationMatrix which wraps another matrix implementation and can display the matrix and provide visual indicators for changes applied to it.
This custom Matrix implementation is also able to slow down the calulation so that it can be watched by humans.