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.

Hiring signal: Understanding of singular value decomposition internals

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: Phase 1, Lessons 01 (Linear Algebra Intuition), 02 (Vectors & Matrices Operations), 03 (Matrix Transformations) Time: ~120 minutes

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 It, Use It, Ship It, Exercises, Key Terms, Further Reading — plus a hands-on lab, quiz, and project artifact.

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