Matrix Transformations

A matrix is a machine that reshapes space. Learn what it does to every point, and you understand the whole transformation.

Build 1.3 hr Python, Julia

Prerequisites: Phase 1, Lessons 01-02 (Linear Algebra Intuition, Vectors & Matrices Operations)

#Learning Objectives

Construct rotation, scaling, shearing, and reflection matrices and apply them to 2D and 3D points
Compose multiple transformations by matrix multiplication and verify that order matters
Compute eigenvalues and eigenvectors of 2x2 matrices from the characteristic equation
Explain why eigenvalues determine PCA directions, RNN stability, and spectral clustering behavior

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The text and code of this lesson are based on AI Engineering from Scratch by Rohit Ghumare, MIT licensed.