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

Vectors, Matrices & Operations

Every neural network is just matrix multiplication with extra steps.

Hiring signal: Understanding of vectors, matrices & operations internals

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: Phase 1, Lesson 01 (Linear Algebra Intuition) Time: ~60 minutes

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

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