This repository contains Python implementations for solving systems of linear equations, finding the inverse of a matrix, and performing matrix decompositions. The following methods are included:
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Gauss-Jordan Elimination: Solves a system of linear equations A x = b and finds the inverse of a matrix A using the Gauss-Jordan elimination method.
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LU Decomposition: Computes the LU decomposition of a matrix A and uses it to solve the system A x = b.
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Cholesky Decomposition: Performs the Cholesky decomposition of a positive-definite matrix A and uses it to solve the system A x = b.
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Comparison: Computes the running time of these solving methods and provides a comparison of their efficiency.
Here is a list of the Python files in this repository:
Choleski_decomposition.py: Python implementation of the Cholesky decomposition.Find_the_inverse_of_a_matrix_by_elimination_of_Gauss.py: Python code to find the inverse of a matrix using the Gauss-Jordan elimination method.Implementation_for_the_LU_decomposition.py: Python implementation of the LU decomposition.Inverse_by_Choleski_decomposition.py: Python code to find the inverse of a matrix using Cholesky decomposition.LU_Inverse.py: Python script for finding the inverse of a matrix using LU decomposition.Solve_a_system_by_LU_decomposition.py: Python script for solving a system of linear equations using LU decomposition.Solve_a_system_by_the_elimination_of-Gauss.py: Python script for solving a system of linear equations using Gauss-Jordan elimination.comparing_these_solving_methods.py: Python script for comparing the efficiency of the different solving methods.
To use these implementations, you can import the relevant Python files into your own projects or run the comparison script to evaluate the performance of the methods.
For a detailed explanation of the algorithms and usage examples, please refer to the Lab_03__Solve_linear_system_and_matrix_decomposition.pdf file in this repository.
We hope you find these implementations useful for your linear algebra and matrix decomposition needs. If you have any questions or encounter any issues, feel free to open an issue in this repository.
Happy linear algebra solving!