Matrix Multiplication Workbook

A hands-on workbook by Prof. Tom Yeh featuring 250+ pages of puzzles and 950+ fill-in-the-blank exercises, designed to help you internalize matrix multiplication by hand ✍️ covering calculation, complexity, shape, identity, scaling, shifting, row and column combinations, non-commutativity, associativity, distributivity, chained products, transpose, inverse, linear equations, and tiled algorithms used in real AI systems.

Key Features:

- You work by hand ✍️, with real numbers

- You fill in the blanks instead of reading proofs

- You reason about shapes, rows, columns, and structure step by step

- You discover the math yourself, rather than being told the rules upfront

Book Description:

Most people learn matrix multiplication by memorizing rules and procedures. They can follow the steps, but they don't really see what's happening. This workbook was created for readers who want something different.

I didn't write this book because matrix multiplication came naturally to me. I struggled with it for years. It felt abstract, mechanical, and easy to get wrong. Even when I got the right answer, I often couldn't tell why it was right.

Later, as I began teaching matrix multiplication, I realized many students were stuck in exactly the same place I had been. This workbook grew out of that struggle. The emphasis is on doing, not memorizing.

Over several years of teaching, this method was refined again and again rewritten whenever something didn't click, simplified whenever an equation added abstraction without insight.

Most people learn matrix multiplication by memorizing rules and procedures. They can follow the steps but they don't really see what's happening. This workbook was created for readers who want something different.

By the end of this workbook, matrix multiplication should no longer feel abstract or fragile. It should feel concrete, reliable, and usable the kind of understanding you can trust when building real systems in AI, graphics, optimization, or data science.

What You Will Learn:

- Multiply matrices confidently using correct shapes and rules

- Recognize identity matrices, scaling, shifting, and their effects

- Understand why matrix multiplication is not commutative

- Apply associativity and distributive properties to simplify work

- Use chaining and transpose concepts in real computations

- Build intuition for inverse matrices and linear equations

- Strengthen speed and accuracy through progressive practice sets

- Learn tiled multiplication ideas for efficient computation

Who this book is for:

This book is ideal for:

- Students learning linear algebra, machine learning, or AI

- Engineers and practitioners who "use" matrices but want deeper intuition

- Educators looking for a concrete, classroom-friendly teaching tool

- Anyone who has learned the rules-but never felt fully confident using them

This is not a reference book and not a collection of proofs. It's a workbook designed to be written in.

Use a pencil. Solve by hand. Make mistakes. Slow down. Learn!

Table of Contents

- Calculate

- Complexity

- Shape

- Identity

- Scale

- Shift

- Combine Rows

- Combine Columns

- Not Commutative

- Associative

- Distributive

- Chain

- Transpose

- Inverse

- Linear Equations

- Tiled Algorithm