May 1, 2024
Updated June 28, 2025
15 minute read
A Comprehensive Guide to Vector Math
Vector math, a fundamental branch of mathematics, is the study of vectors—objects that possess both magnitude and direction. At a high level, you can think of a vector as an arrow pointing in a specific direction with a certain length. This simple concept is the bedrock of many advanced fields, allowing us to model and manipulate quantities in two, three, or even thousands of dimensions. From the physics that governs motion to the algorithms that render stunning virtual worlds, vectors provide a language to describe and interact with our surroundings in a precise, mathematical way.
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Find a path to becoming a Vector Math. Learn more at:
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Reading list
We've selected 22 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Vector Math.
Connects linear algebra directly to the concepts and methods used in machine learning and neural networks. It valuable resource for those looking to apply their vector math knowledge to contemporary topics in artificial intelligence. It is suitable for advanced undergraduate students, graduate students, and professionals.
Is specifically tailored for those interested in the applications of vector math in computer graphics and game development. It covers essential topics like vectors, matrices, transformations, and quaternions with a practical approach. It is an excellent resource for undergraduate students and professionals in these fields.
The first volume of this series is dedicated to the mathematical concepts required for game engine development, with a significant focus on vector and matrix math. It provides a deep dive into the mathematical underpinnings needed for 3D graphics and physics, making it highly relevant for professionals and advanced students.
Is widely regarded as an excellent introductory text for linear algebra, which forms the foundation of vector math. It provides a solid broad understanding with a focus on the four fundamental subspaces. It is commonly used as a textbook in undergraduate programs and is valuable for self-study.
Covers the fundamental mathematical tools, including linear algebra and vector calculus, necessary for understanding machine learning algorithms. It bridges the gap between mathematical theory and machine learning applications, making it ideal for students and professionals in data science and AI.
Provides a practical introduction to linear algebra with a focus on vectors, matrices, and least squares, with applications in data analysis, statistics, and related fields. It is suitable for undergraduate students and professionals seeking a hands-on approach to vector math applications.
This textbook provides a comprehensive introduction to linear algebra with a balance of theory and applications. It is well-suited for undergraduate students and includes many examples and exercises that demonstrate the practical uses of vector math in various fields.
Presents Geometric Algebra as an alternative framework for geometric computing, extending linear algebra to provide a more unified and powerful approach to vector math in 3D applications. It is highly relevant for those in computer graphics, robotics, and game development seeking advanced techniques.
Provides a geometric approach to linear algebra, emphasizing linear transformations. It widely used textbook for undergraduate courses and offers a good balance of theory and applications, making vector math concepts more intuitive.
Offers a modern introduction to linear algebra with a focus on visualization and applications. It connects vector math to various fields, including physics, engineering, and computer science, making it engaging for undergraduate students. It useful reference and textbook.
A widely used introductory textbook for linear algebra. It provides a clear and accessible introduction to vector math concepts with a strong emphasis on computational aspects and a broad range of applications. Suitable for high school and early undergraduate students.
Emphasizes the practical applications of linear algebra and vector math in various scientific and engineering disciplines. It is suitable for advanced undergraduate and graduate students and professionals who need to apply linear algebra to solve real-world problems.
Offers a more abstract and theoretical approach to linear algebra, focusing on vector spaces and linear maps without relying heavily on determinants initially. It is suitable for those looking to deepen their understanding of the underlying theory and is often used in upper-level undergraduate or introductory graduate courses.
Authored by the renowned Gilbert Strang, this newer book aims to make linear algebra accessible to a wider audience, including those without a strong mathematical background. It focuses on the most essential concepts and their applications in data analysis, making it relevant for beginners and professionals in data-driven fields.
A classic textbook offering a rigorous and comprehensive treatment of linear algebra. It is suitable for advanced undergraduate and graduate students seeking a deep theoretical understanding of vector spaces, linear transformations, and related concepts.
This free, open-source textbook for a first undergraduate course in linear algebra. It covers the essential topics of vector spaces, linear maps, and matrices with a focus on motivation and computational examples, making it a good resource for broad understanding and practice.
A classic and elegant theoretical treatment of finite-dimensional vector spaces. is concise and abstract, focusing on the fundamental concepts from a purely mathematical perspective. It is valuable for those seeking a deep theoretical understanding and is suitable for advanced students.
While focusing on calculus, this book provides a strong foundation in vector operations, vector fields, and theorems related to vector calculus. It is essential for understanding the behavior of vectors in higher dimensions and is typically used in undergraduate physics and engineering programs. is more valuable as additional reading than a current reference.
This comprehensive graduate-level text focusing on matrix theory, which is deeply intertwined with vector math. It valuable reference for those needing a deep understanding of matrix properties and decompositions. is for advanced students and researchers.
While a broader algebra text, this book integrates linear algebra throughout and provides a strong foundation in abstract algebraic concepts relevant to vector spaces and linear transformations. It is suitable for advanced undergraduate and graduate students.
While a calculus book, it includes significant coverage of vectors in 2D and 3D space, vector functions, and vector calculus. It provides essential background knowledge for understanding vector math in a calculus context and standard textbook in undergraduate science and engineering programs.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/vmvefk/vector
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