1. Front Matter
Pages i-xxv
2. Peter J. Olver, Chehrzad Shakiban
Pages 1-74
3. Peter J. Olver, Chehrzad Shakiban
Pages 75-128
4. Peter J. Olver, Chehrzad Shakiban
Pages 129-182
5. Peter J. Olver, Chehrzad Shakiban
Pages 183-234
6. Peter J. Olver, Chehrzad Shakiban
Pages 235-300
7. Peter J. Olver, Chehrzad Shakiban
Pages 301-340
8. Peter J. Olver, Chehrzad Shakiban
Pages 341-402
9. Peter J. Olver, Chehrzad Shakiban
Pages 403-474
10. Peter J. Olver, Chehrzad Shakiban
Pages 475-563
11. Peter J. Olver, Chehrzad Shakiban
Pages 565-632
12. Back Matter
Pages 633-679

### Introduction

This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics.

Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the underlying linear algebraic techniques, thereby enabling students not only to learn how to apply the mathematical tools in routine contexts, but also to understand what is required to adapt to unusual or emerging problems.

No previous knowledge of linear algebra is needed to approach this text, with single-variable calculus as the only formal prerequisite. However, the reader will need to draw upon some mathematical maturity to engage in the increasing abstraction inherent to the subject. Once equipped with the main tools and concepts from this book, students will be prepared for further study in differential equations, numerical analysis, data science and statistics, and a broad range of applications. The first author’s text, Introduction to Partial Differential Equations, is an ideal companion volume, forming a natural extension of the linear mathematical methods developed here.

### Keywords

Linear algebra Vector spaces Inner products and norms Equilibrium Eigenvalues and singular values Linear systems Linear algebra textbook Peter Olver textbook Applied linear algebra Principle component analysis Linear iterative systems Dynamical systems

#### Authors and affiliations

• Peter J. Olver
• 1
• 2
1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
2. 2.Department of MathematicsUniversity of St. ThomasSt. PaulUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-91041-3
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-319-91040-6
• Online ISBN 978-3-319-91041-3
• Series Print ISSN 0172-6056
• Series Online ISSN 2197-5604
• Buy this book on publisher's site
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