Matrix Multiplication Workbook: Fill-in-the-Blank Puzzles to Build Real Intuition by Hand

Matrix Multiplication Workbook: Fill-in-the-Blank Puzzles to Build Real Intuition by Hand

If matrix multiplication still feels mechanical or unclear, this book is for you. Build real intuition with 950+ fill-in-the-blank exercises designed for pencil-and-paper practice. Master shapes, identity, scaling, chaining, transpose, inverse, and tiled algorithms used in AI, machine learning, and data science. Book Description “What we should do is learn kind of basic things in mathematics, in modeling, mathematics that can be connected with reality”. Yann LeCun, on The Information Bottleneck Podcast Most people learn matrix multiplication by memorizing rules and procedures. They can follow the steps, but they don’t really see what’s happening especially when the shapes change or the multiplication chains get longer. When I began teaching, I realised many students were stuck. They could compute, but they didn’t feel confident. This workbook is a product of that experience. The emphasis here is on doing, not memorizing. You won’t read long proofs. Instead, you’ll fill in carefully designed blanks step by step, reasoning about shapes, rows, columns, and structure as you go. You’ll fill in missing dimensions, intermediate steps, and partial results not just final answers. The goal isn’t just to get answers. It’s to build intuition you can trust, so you can catch mistakes earlier and know what a product should look like before you finish it. By the end of this workbook, matrix multiplication should no longer feel fragile. This is not a reference book. It’s meant to be written in. Use a pencil. Work slowly. Make mistakes. That’s how you learn. 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 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 “This book guides the reader through hundreds of fill-in-the-blank matrix puzzles, ranging from simple matrix arithmetic to the deep applications that drive neural networks and machine learning —the core math powering computer vision, self-driving vehicles, natural language processing, and generative AI." Kirk Borne, Data Scientist, Educator, Advisor to AI startups and founder of LeadershipData “Tom Yeh's Deep Learning Math Workbook focuses entirely on matrix multiplication across 16 chapters and 263 pages. Every exercise is hands-on. You fill in grids, trace computations cell by cell, and build the muscle memory that makes matrix operations intuitive rather than abstract.” Jason Strimpel, Managing Director, AI & Advanced Analytics | Author of Python for Algorithmic Trading Cookbook “For anyone serious about machine learning, mastering linear algebra is non-negotiable, and this interactive, puzzle-driven approach makes even advanced topics feel accessible and engaging. You don’t just learn the concepts. You ACTUALLY enjoy practicing them!” Serg Masis, Principal AI Scientist, Author of Interpretable Machine Learning with Python “For anyone serious about machine learning, mastering linear algebra is non-negotiable, and this interactive, puzzle-driven approach makes even advanced topics feel accessible and engaging. You don’t just learn the concepts. You ACTUALLY enjoy practicing them!” Serg Masis, Principal AI Scientist, Author of Interpretable Machine Learning with Python Tom Yeh is an Associate Professor of Computer Science at the University of Colorado Boulder, specializing in human computer interaction and its societal impacts.