Generate figures of vector space generated from the columns of two 3-dimensions matrix with rank = 3 and rank = 2

matrix_rank.py

import numpy as np
import matplotlib.pyplot as plt


def main() -> None:
    # Define the matrices
    W1 = np.eye(3)  # Identity matrix
    W2 = np.array([[3, -2, 1], [2, -2, 0], [0, 1, 1]])  # Rank-deficient matrix

    # Create figure for W1
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    origin = [0, 0, 0]
    ax.quiver(*origin, W1[:, 0], W1[:, 1], W1[:, 2], color=['b', 'g', 'r'])
    ax.set_xlim([-1, 2])
    ax.set_ylim([-1, 2])
    ax.set_zlim([-1, 2])
    ax.set_title('Vector Space Generated by W1 (r = 3)')
    plt.show()

    # Create figure for W2
    fig, ax = plt.subplots()
    ax.quiver(0, 0, W2[0, 0], W2[1, 0], angles='xy', scale_units='xy', scale=1, color='b', label='C1')
    ax.quiver(0, 0, W2[0, 1], W2[1, 1], angles='xy', scale_units='xy', scale=1, color='g', label='C2')
    ax.quiver(0, 0, W2[0, 2], W2[1, 2], angles='xy', scale_units='xy', scale=1, color='r',
              label='C3 - Linear Combination of C1 and C2')
    ax.set_xlim([-3, 4])
    ax.set_ylim([-3, 4])
    ax.set_aspect('equal')
    ax.set_title('Vector Space Generated by W2 (r = 2)')
    ax.legend()
    plt.show()


if __name__ == '__main__':
    main()