Phase 0: Linear Algebra Foundations · ~60 minutes · Python · Julia

Linear Algebra Intuition

Every AI model is just matrix math wearing a fancy hat.

What you will learn

Implement vector and matrix operations (addition, dot product, matrix multiply) from scratch in Python
Explain geometrically what the dot product, projection, and Gram-Schmidt process do
Determine linear independence, rank, and basis of a set of vectors using row reduction
Connect linear algebra concepts to their AI applications: embeddings, attention scores, and LoRA

Introduction

Type: Learn
Languages: Python, Julia
Prerequisites: Earlier lessons in this course
Time: ~60 minutes

Objective

Learning objectives

Implement vector and matrix operations (addition, dot product, matrix multiply) from scratch in Python
Explain geometrically what the dot product, projection, and Gram-Schmidt process do
Determine linear independence, rank, and basis of a set of vectors using row reduction
Connect linear algebra concepts to their AI applications: embeddings, attention scores, and LoRA

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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Key terms in this lesson

LoRA (Low-Rank Adaptation)