Editing Linear Algebra (section)

== <span style="color: #FFFFFF;">Applying</span> ==
'''Modeling 'Image Transformations' (Scaling and Rotating):'''
<syntaxhighlight lang="python">
import numpy as np

def transform_point(x, y, scale_factor, rotation_deg):
    """
    Shows how a Matrix 'moves' a point.
    """
    theta = np.radians(rotation_deg)
    # The Rotation Matrix
    R = np.array([
        [np.cos(theta), -np.sin(theta)],
        [np.sin(theta),  np.cos(theta)]
    ])
    
    # The Scale Matrix
    S = np.array([
        [scale_factor, 0],
        [0, scale_factor]
    ])
    
    point = np.array([x, y])
    # Apply Scale then Rotation
    new_point = R @ S @ point
    return new_point

# Move point [1, 0] by scaling 2x and rotating 90 deg
print(f"New Position: {transform_point(1, 0, 2, 90)}")
# This is how GPUs render 3D games and movies.
</syntaxhighlight>

; Linear Algebra in Tech
: '''Data Compression (SVD)''' → Breaking a giant matrix (like an image) into smaller ones to save space without losing detail.
: '''Principal Component Analysis (PCA)''' → Finding the most important "directions" in a massive dataset to simplify it.
: '''Deep Learning''' → Every layer of a neural network is just a "Matrix Multiplication" followed by a small non-linear tweak.
: '''Cryptography''' → Using matrix operations that are easy to do but "hard to undo" without a key (Lattice-based crypto).
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