Phase 0: Linear Algebra Foundations · ~75 minutes · Python · Julia

Matrix Transformations

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

What you will learn

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

Introduction

Type: Build
Languages: Python, Julia
Prerequisites: Linear Algebra Intuition
Time: ~75 minutes

Objective

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

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.

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