Chapter 3

Matrices

Matrices as tables, shape rules, linear maps, and neural network layers.

What this chapter does

Matrices organize many vectors at once. This chapter teaches shape discipline first, then shows how row-column products become transformations, batches, and the weight matrices used in neural network layers.

Lessons

Read these in order.

Start with the chapter introduction, then move through the topic lessons. The order is chosen so each page can reuse ideas from the pages before it.

01
Introduction
Why matrices follow vectors and how shape-aware tables organize computation.
02
Matrices as Tables
Matrix entries, rows, columns, and row-column indexing.
03
Rows, Columns, and Shapes
How matrix shape controls what operations are allowed.
04
Matrix-Vector Products
Reading matrix-vector multiplication as one dot product per row.
05
Matrix Multiplication
Matrix products as repeated row-column dot products.
06
Identity, Diagonal, and Transpose
Three matrix patterns that appear throughout ML equations.
07
Batches and Shape Reasoning
Reading examples-by-features matrices and predicting batch outputs.
08
Matrices as Linear Maps
Matrices as operations that transform input vectors into output vectors.
09
Matrices in Neural Network Layers
How weight matrices mix features inside a basic neural network layer.

Review and practice

Close the chapter deliberately.

Use the conclusion and revision notes before the chapter exercises. Hints and solutions are collected here, while lesson-level exercises reveal their own help inline.

Conclusion

What Chapter 3 accomplished and how matrices prepare geometry.

Summary and Revision Notes

A compact review of matrix notation, shapes, and common traps.

Exercises

Chapter-level practice for matrix entries, shapes, and products.

Hints

Low-spoiler nudges for the Chapter 3 exercises.

Solutions

Explained solutions for the Chapter 3 exercises.