Full Description
Full colour workbook by Prof. Tom Yeh featuring 250+ pages of puzzles and 950+ fill-in-the-blank exercises.
It is 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 DescriptionMost 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 forThis 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!
Contents
Table of Contents
Calculate
Complexity
Shape
Identity
Scale
Shift
Combine Rows
Combine Columns
Not Commutative
Associative
Distributive
Chain
Transpose
Inverse
Linear Equations
Tiled Algorithm
