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Think Linear Algebra (2023)

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Why This Matters

Think Linear Algebra offers a practical, code-first approach to mastering linear algebra through real-world applications and hands-on coding with Python. It emphasizes intuitive understanding and immediate application, making complex concepts accessible for learners and professionals alike. This approach is especially valuable given linear algebra's critical role in advancing fields like machine learning, scientific computing, and computer graphics.

Key Takeaways

Think Linear Algebra#

Think Linear Algebra is a code-first, case-based introduction to the most widely used concepts in linear algebra, designed for readers who want to understand and apply these ideas — not just learn them in the abstract. Each chapter centers on a real-world problem like modeling traffic in the web, simulating flocking birds, or analyzing electrical circuits. Using Python and powerful libraries like NumPy, SciPy, SymPy, and NetworkX, readers build working solutions that reveal how linear algebra provides elegant, general-purpose tools for thinking and doing.

Press the play button to try this example from the chapter on affine transforms.

This book is for readers who may have struggled with traditional math instruction, or who want a more intuitive, hands-on way to learn. By working in Jupyter notebooks, readers get instant feedback as they write code, run simulations, visualize results, and explore what-if scenarios. Rather than beginning with mathematical formalism, Think Linear Algebra starts with meaningful applications and builds up the theory when it’s needed. The result is a uniquely practical and empowering introduction to linear algebra as a language for solving real problems.

Linear algebra is foundational for machine learning, scientific computing, and computer graphics — fields with enormous demand and growth. From search engines and GPS tracking to signal processing and structural engineering, linear algebra is the language behind many of the technologies that shape our world. This book shows you how to use it effectively in your own work.

This book is available under a Creative Commons license, which means that you are free to copy, distribute, and modify it, as long as you attribute the source and don’t use it for commercial purposes.