Eigenvector Analysis using Python

This project explores the eigenstructure of a 2x2 matrix using Python, focusing on calculating and visualizing eigenvectors and their transformations.

Overview

We:

• Define a matrix A
• Compute its eigenvalues and eigenvectors
• Normalize the eigenvectors
• Visualize the original and transformed vectors using matplotlib

This process helps us understand the geometric interpretation of eigenvectors under linear transformation.

Files

• eigenvector_analysis.ipynb — Jupyter Notebook with code and plots
• eigenvectors_report.tex — LaTeX report with detailed explanation and figure
• eigenvectors_plot.png — Generated plot showing eigenvectors and their transformation
• README.md — This file

Requirements

Install the required packages using:

pip install numpy matplotlib

Running the Code

1. Open the notebook or script.
2. Execute all cells or run the script.
3. A plot will be generated and saved as eigenvectors_plot.png.

Output Preview

The generated plot displays:

• Red/Blue Arrows: Normalized eigenvectors
• Green/Yellow Arrows: Transformed vectors ( A \cdot v )

Visualization

The figure below shows the normalized eigenvectors of matrix A and their transformations:

License

MIT License