Part of Cambridge Mathematical Textbooks
- Elizabeth S. Meckes, Case Western Reserve University, Ohio
- Mark W. Meckes, Case Western Reserve University, Ohio
Linear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.Read more
- Introduces central topics, such as vector spaces, linear maps, linear dependence and eigenvalues early in the book with the aim of helping students transition from calculus to rigorous mathematics
- Motivates the reader whilst introducing new topics, definitions, and appropriate examples in connection with the core concepts presented early in the text so that students will be able to go back to these vital notions and, by the time the course ends, will have worked with them extensively
- Includes many pedagogical features, such as: 'Quick Exercises' throughout with answers upside-down at the bottom of the page; periodic 'Perspectives' that collect various viewpoints on particular topics developed throughout the text; and numerous in-text examples, end-of-chapter exercises, and hints and answers to selected problems at the end of the book
Reviews & endorsements
'This is a book for anyone who wants to really understand linear algebra. Instead of mere cookbook recipes or dry proofs, it provides explanations, examples, pictures - and, yes, algorithms and proofs too, but only after the reader is able to understand them. And while it is aimed at beginners, even experts will have something to learn from this book.' John Baez, University of California, RiversideSee more reviews
'This is an exciting and entertaining book. It keeps an informal tone, but without sacrificing accuracy or clarity. It takes care to address common difficulties (and the classroom testing shows), but without talking down to the reader. It uses the modern understanding of how to do linear algebra right, but remains accessible to first-time readers.' Tom Leinster, University of Edinburgh
'Linear algebra is one of the most important topics in mathematics, as linearity is exploited throughout applied mathematics and engineering. Therefore, the tools from linear algebra are used in many fields. However, they are often not presented that way, which is a missed opportunity. The authors have written a linear algebra book that is useful for students from many fields (including mathematics). A great feature of this book is that it presents a formal linear algebra course that clearly makes (coordinate) matrices and vectors the fundamental tools for problem solving and computations.' Eric de Sturler, Virginia Polytechnic Institute and State University
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- Date Published: April 2018
- format: Adobe eBook Reader
- isbn: 9781316836026
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. Linear systems and vector spaces
2. Linear maps and matrices
3. Linear independence, bases, and coordinates
4. Inner products
5. Singular value decomposition and the spectral theorem
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