Matrix_Tools

Matrix_Tools is a collection of Python scripts designed to perform foundational matrix operations with applications in linear algebra, numerical methods, and algorithmic problem-solving. This repository demonstrates both numerical and symbolic computation by leveraging the power of numpy and sympy.

Key Features

• Determinant Calculations: Quickly compute determinants of square matrices.
• Matrix Inversion & Linear Systems: Solve systems using matrix inversion.
• LU Decomposition: Decompose matrices and compute inverses using L⁻¹·U⁻¹.
• Elementary Matrices: Perform and visualize row operations.
• Dot Products & Vector Angles: Calculate dot products and determine angles between vectors.
• Cramer’s Rule: Solve 2x2 and 3x3 linear systems using Cramer’s Rule.

Contents

File	Description
linear_algebra_toolkit.py	Interactive tool for computing determinants, inverses, cofactors, etc.
Matrix_Inversion.py	Solves linear systems using the matrix inversion method.
LU_Decomposition.py	Performs LU decomposition and computes the inverse via L⁻¹·U⁻¹.
Elementary_Matrix.py	Demonstrates row operations using elementary matrices.
Cramers_2x2.py	Solves a 2x2 system using Cramer’s Rule.
Cramers_3x3.py	Solves a 3x3 system using Cramer’s Rule.
DotAngle.py	Computes the angle between two vectors using the dot product.

Requirements

Runtime

To run the matrix tools:

• Python 3.7 or higher
• numpy
• sympy

Install with:

pip install numpy sympy

Usage

Clone the repository:

git clone https://github.com/Anthony-Hackman/Matrix_Tools.git
cd Matrix_Tools

Run the interactive CLI tool:

python linear_algebra_toolkit.py

Alternatively, you can execute any standalone script included. For example:

python Matrix_Inversion.py

Purpose

This repository was created to serve as both an educational tool and a practical resource for experimenting with linear algebra operations. It is intended to support:

• Students learning about matrix computations and linear algebra.
• Developers experimenting with matrix-based algorithms.
• Enthusiasts exploring both numerical and symbolic matrix manipulations.

Contributing

Contributions are welcome! If you have ideas for improvements, bug fixes, or new features, please feel free to open an issue or submit a request.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Author

Anthony Hackman
March 2025