Norms of Matrices and Pseudo-Inverse Matrices

This repository contains Python code to generate random 3x6 matrices, calculate their norms, compute their pseudo-inverses, and compare the norms of both matrices. The goal is to explore any regularity or additivity between the norms of these matrices.

Overview

This program investigates the relationship between the norms of randomly generated 3x6 matrices and the norms of their corresponding pseudo-inverse matrices. We perform the following steps for 10,000 iterations:

1. Generate a random 3x6 matrix with elements in the interval [-1, 1].
2. Calculate the norm of the random matrix.
3. Compute the pseudo-inverse of the random matrix.
4. Calculate the norm of the pseudo-inverse matrix.

The norms of both matrices are plotted as histograms using Matplotlib to visualize any regularities or additivity.

Requirements

To run this code, you need the following Python libraries installed:

• NumPy
• Matplotlib

Program usage

Command to run the Python script:

python matrix_norm_comparison.py

The script will generate the histograms and save the results as an image file (matrix_comparison_histogram.png) in the same directory.