# Applied Linear Algebra and Matrix Analysis

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

1. Front Matter
Pages i-xii
2. Thomas S. Shores
Pages 1-64
3. Thomas S. Shores
Pages 65-180
4. Thomas S. Shores
Pages 181-276
5. Thomas S. Shores
Pages 277-330
6. Thomas S. Shores
Pages 331-390
7. Thomas S. Shores
Pages 391-444
8. Back Matter
Pages 445-479

### Introduction

In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems.

The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces.

Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and Matrix Analysis augments the key elements of linear algebra with a wide choice of optional sections. With the book’s selection of applications and platform-independent assignments, instructors can tailor the curriculum to suit specific interests and ensure students across various disciplines are equipped with the powerful tools of linear algebra.

### Keywords

Gaussian elimination singular value decomposition Gram-Schmidt algorithm orthogonal diagonalization vector spaces discrete dynamical systems matrix algebra operator norms applied linear algebra textbook Google PageRank linear programming digital signal processing diffusive processes

#### Authors and affiliations

1. 1.Department of MathematicsUniversity of Nebraska–LincolnLincolnUSA

Thomas S. Shores is Professor Emeritus of Mathematics at the University of Nebraska–Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.

### Bibliographic information

• Book Title Applied Linear Algebra and Matrix Analysis
• Authors Thomas S. Shores
• Series Title Undergraduate Texts in Mathematics
• Series Abbreviated Title Undergraduate Texts Mathematics
• DOI https://doi.org/10.1007/978-3-319-74748-4
• Copyright Information Springer International Publishing AG, part of Springer Nature 2018
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-319-74747-7
• Softcover ISBN 978-3-030-09067-8
• eBook ISBN 978-3-319-74748-4
• Series ISSN 0172-6056
• Series E-ISSN 2197-5604
• Edition Number 2
• Number of Pages XII, 479
• Number of Illustrations 15 b/w illustrations, 30 illustrations in colour
• Topics
• Buy this book on publisher's site
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