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

Vectors, Matrices & Operations

Every neural network is just matrix multiplication with extra steps.

What you will learn

Build a Matrix class with element-wise operations, matrix multiplication, transpose, determinant, and inverse
Distinguish element-wise multiplication from matrix multiplication and explain when each applies
Implement a single dense neural network layer (`relu(W @ x + b)`) using only the from-scratch Matrix class
Explain broadcasting rules and how bias addition works in neural network frameworks

Introduction

Type: Build
Languages: Python, Julia
Prerequisites: Linear Algebra Intuition
Time: ~60 minutes

Objective

Learning objectives

Build a Matrix class with element-wise operations, matrix multiplication, transpose, determinant, and inverse
Distinguish element-wise multiplication from matrix multiplication and explain when each applies
Implement a single dense neural network layer (relu(W @ x + b)) using only the from-scratch Matrix class
Explain broadcasting rules and how bias addition works in neural network frameworks

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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