Matrix Multiplication Workbook

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 FeaturesYou work by hand ✍️, with real numbersYou fill in the blanks instead of reading proofsYou reason about shapes, rows, columns, and structure step by stepYou discover the math yourself, rather than being told the rules upfrontBook 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 learnMultiply matrices confidently using correct shapes and rulesRecognize identity matrices, scaling, shifting, and their effectsUnderstand why matrix multiplication is not commutativeApply associativity and distributive properties to simplify workUse chaining and transpose concepts in real computationsBuild intuition for inverse matrices and linear equationsStrengthen speed and accuracy through progressive practice setsLearn tiled multiplication ideas for efficient computationWho 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!