Example vector subspace for the book "Practical Linear Algebra for Data Science"

vector_subspace_example.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Define the vectors
v1 = np.array([1, 0, 2])
v2 = np.array([-1, 2, 3])

# Create a grid of values for t1 and t2
t1, t2 = np.mgrid[-1:1:0.1, -1:1:0.1]

# Ensure t1 and t2 have compatible shapes for broadcasting
t1 = t1.flatten()
t2 = t2.flatten()

# Create points in the subspace by taking linear combinations of v1 and v2
points = t1[:, np.newaxis] * v1 + t2[:, np.newaxis] * v2

# Extract x, y, and z coordinates
x, y, z = points[:, 0], points[:, 1], points[:, 2]

# Create the 3D plot
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x, y, z, s=2)

# Add arrows for the vectors
ax.quiver(0, 0, 0, v1[0], v1[1], v1[2], color='r', label='v1', arrow_length_ratio=0.3)
ax.quiver(0, 0, 0, v2[0], v2[1], v2[2], color='g', label='v2', arrow_length_ratio=0.3)

# Set labels and title
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Subspace of Vectors [1, 0, 2] and [-1, 2, 3]')
plt.legend()  # Show the legend

# Display the plot
plt.show()