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Look Inside Linear Algebra

Linear Algebra

Part of Cambridge Mathematical Textbooks

Authors:
Elizabeth S. Meckes, Case Western Reserve University, Ohio
Mark W. Meckes, Case Western Reserve University, Ohio

Date Published: April 2018
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9781316836026

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About the Authors

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.
- 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
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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, Riverside
'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
'It is a book well worth considering both for learning and teaching this important area of mathematics.' John Baylis, The Mathematical Gazette
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Product details
- 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
6. Determinants.
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Authors
Elizabeth S. Meckes, Case Western Reserve University, Ohio
Elizabeth S. Meckes is Associate Professor at Case Western Reserve University, Ohio. Her research is in probability and analysis, with an emphasis on random matrix theory. She received her bachelor's (2001) and master's (2002) degrees at Case Western Reserve University, and her doctoral degree (2006) at Stanford University. She is currently writing a monograph on random matrices (Cambridge, forthcoming).
Mark W. Meckes, Case Western Reserve University, Ohio
Mark W. Meckes is Associate Professor at Case Western Reserve University, Ohio. His research is in analysis and probability, focusing on random matrix theory and metric geometry. He received his bachelor's (1999) and doctoral (2003) degrees at Case Western Reserve University, Ohio.