Phase 0: Linear Algebra Foundations · ~120 minutes · Python · Julia

Singular Value Decomposition

SVD is the Swiss Army knife of linear algebra. Every matrix has one. Every data scientist needs one.

What you will learn

Implement SVD via power iteration and explain the geometric meaning of U, Sigma, and V^T
Apply truncated SVD for image compression and measure the compression ratio vs reconstruction error
Compute the Moore-Penrose pseudoinverse via SVD to solve overdetermined least-squares systems
Connect SVD to PCA, recommendation systems (latent factors), and Latent Semantic Analysis in NLP

Introduction

Type: Build
Languages: Python, Julia
Prerequisites: Linear Algebra Intuition, Matrix Transformations
Time: ~120 minutes

Objective

Learning objectives

Implement SVD via power iteration and explain the geometric meaning of U, Sigma, and V^T
Apply truncated SVD for image compression and measure the compression ratio vs reconstruction error
Compute the Moore-Penrose pseudoinverse via SVD to solve overdetermined least-squares systems
Connect SVD to PCA, recommendation systems (latent factors), and Latent Semantic Analysis in NLP

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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