May 1, 2024
Updated May 8, 2025
21 minute read
Linear transformations are a fundamental concept in mathematics, particularly in the field of linear algebra. At a high level, a linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. This means that if you take two vectors, add them together, and then apply the transformation, you get the same result as if you transformed each vector individually and then added the results. Similarly, if you scale a vector by a number and then apply the transformation, it's the same as transforming the vector first and then scaling it. This elegant property makes linear transformations incredibly powerful for understanding and manipulating data in a structured way.
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Reading list
We've selected 35 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
Linear Transformations.
This comprehensive textbook provides a thorough introduction to linear algebra, covering topics such as vector spaces, matrices, and linear transformations. It is suitable for both undergraduate and graduate students and is written in a clear and accessible style.
This graduate-level textbook provides a comprehensive and rigorous introduction to advanced linear algebra, with a focus on topics such as multilinear algebra, tensor analysis, and representation theory. It is written in a clear and concise style and is suitable for students with a strong background in linear algebra.
This graduate-level textbook provides a comprehensive and rigorous introduction to matrix theory, with a focus on topics such as matrix algebra, matrix analysis, and matrix applications. It is written in a clear and concise style and is suitable for students with a strong background in linear algebra.
This undergraduate-level textbook provides a rigorous and comprehensive introduction to linear algebra, with a focus on proofs and abstract concepts. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
This best-selling textbook offers a novel approach to linear algebra by delaying the introduction of determinants and focusing on understanding the structure of linear operators (linear transformations) on finite-dimensional vector spaces. It is highly regarded for its clarity and theoretical depth, making it excellent for deepening understanding at the undergraduate and graduate levels. The 4th edition is available open access.
This comprehensive graduate-level book focuses on matrix theory, which is intimately connected to linear transformations. It standard reference for advanced topics and provides a deep understanding of the properties and applications of matrices and linear operators in finite-dimensional vector spaces.
This undergraduate-level textbook provides a rigorous introduction to linear transformations and matrices, with a focus on applications in engineering and physics. It covers topics such as eigenvalues, eigenvectors, and matrix diagonalization.
This undergraduate-level textbook provides a comprehensive and accessible introduction to linear algebra, with a focus on applications in engineering, the sciences, and economics. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and engaging style.
This undergraduate-level textbook provides a comprehensive and accessible introduction to linear algebra, with a focus on applications in engineering and the sciences. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
This undergraduate-level textbook provides a comprehensive and accessible introduction to linear algebra, with a focus on applications in engineering and the sciences. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
Considered a classic in the field, this book provides a rigorous and abstract treatment of linear algebra. It is well-suited for advanced undergraduates and graduate students seeking a deep theoretical understanding of vector spaces and linear transformations. While older, its comprehensive coverage and clear style make it a valuable reference.
This undergraduate-level textbook provides a comprehensive and accessible introduction to linear algebra, with a focus on applications in engineering and the sciences. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
This undergraduate-level textbook provides a rigorous and comprehensive introduction to linear transformations, with a focus on applications in engineering and the sciences. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
A comprehensive graduate-level text covering a wide range of advanced topics in linear algebra, including modules, canonical forms, and multilinear algebra. It provides a deeper theoretical understanding of the structures underlying linear transformations and vector spaces. Suitable for graduate students in mathematics.
Provides an elegant and insightful treatment of linear algebra with a focus on functional analysis. It covers core topics and delves into more advanced subjects, making it suitable for graduate students and researchers. It offers a deep perspective on linear transformations within a broader mathematical context.
A foundational text in numerical linear algebra, this book delves into the algorithms and computational aspects of matrix operations and linear transformations. It comprehensive reference for graduate students and professionals working with large-scale numerical problems.
A popular and widely adopted textbook for introductory linear algebra courses. emphasizes the connections between linear transformations and matrix equations, providing numerous examples and applications across various fields. It is suitable for undergraduates and helps solidify understanding through practice.
A concise and classic text that presents linear algebra from a purely abstract vector space viewpoint. is highly valued for its elegant style and focus on the essential concepts of linear transformations without relying heavily on matrices. It is excellent for deepening theoretical understanding, particularly for graduate students.
Offers a comprehensive treatment of matrix analysis with a strong emphasis on applications. It bridges the gap between theory and practice, showing how linear algebra concepts, including linear transformations, are used to solve problems in various disciplines. Suitable for advanced undergraduates and graduate students in applied fields.
Another classic text offering an abstract approach to linear algebra. covers fundamental concepts, including vector spaces and linear mappings, in a concise and rigorous manner. It is suitable for advanced undergraduates and graduate students and good resource for deepening theoretical understanding.
This undergraduate-level textbook provides a clear and accessible introduction to linear algebra, with a focus on applications in engineering and the sciences. It covers topics such as vector spaces, matrices, and linear transformations, and is written in a clear and concise style.
Is widely considered a standard introductory textbook for linear algebra. It provides a solid foundation in the basic concepts, including linear transformations, with a focus on understanding the mechanics and applications. It is commonly used as a textbook in undergraduate programs and is valuable for gaining a broad understanding.
Provides an excellent introduction to the numerical aspects of linear algebra, including the practical implementation and computational considerations of working with linear transformations and matrices. It is suitable for advanced undergraduates and graduate students interested in the computational side of the subject.
Offers a more abstract and geometric approach to linear algebra, covering topics such as multilinear algebra and exterior algebra in addition to standard concepts like linear transformations. It is suitable for advanced undergraduate and graduate students interested in the deeper mathematical structures.
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