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Applied Linear Algebra and Matrix Methods

  • Textbook
  • © 2023

Overview

Authors:
  1. Timothy G. Feeman

    1. Department of Mathematics and Statistics, Villanova University, Villanova, USA

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  • Presents powerful linear algebra tools in the context of real-world applications
  • Incorporates computers to implement algorithms for engaging projects
  • sn.pub/extras

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Vectors

    • Timothy G. Feeman
    Pages 1-46

  3. Matrices

    • Timothy G. Feeman
    Pages 47-72

  4. Matrix Contexts

    • Timothy G. Feeman
    Pages 73-120

  5. Linear Systems

    • Timothy G. Feeman
    Pages 121-165

  6. Least Squares and Matrix Geometry

    • Timothy G. Feeman
    Pages 167-198

  7. Orthogonal Systems

    • Timothy G. Feeman
    Pages 199-221

  8. Eigenvalues

    • Timothy G. Feeman
    Pages 223-247

  9. Markov Processes

    • Timothy G. Feeman
    Pages 249-268

  10. Symmetric Matrices

    • Timothy G. Feeman
    Pages 269-284

  11. Singular Value Decomposition

    • Timothy G. Feeman
    Pages 285-313

  12. Back Matter

    Pages 315-321
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Keywords

About this book

This textbook is designed for a first course in linear algebra for undergraduate students from a wide range of quantitative and data driven fields. By focusing on applications and implementation, students will be prepared to go on to apply the power of linear algebra in their own discipline. With an ever-increasing need to understand and solve real problems, this text aims to provide a growing and diverse group of students with an applied linear algebra toolkit they can use to successfully grapple with the complex world and the challenging problems that lie ahead. Applications such as least squares problems, information retrieval, linear regression, Markov processes, finding connections in networks, and more, are introduced on a small scale as early as possible and then explored in more generality as projects. Additionally, the book draws on the geometry of vectors and matrices as the basis for the mathematics, with the concept of orthogonality taking center stage. Important matrixfactorizations as well as the concepts of eigenvalues and eigenvectors emerge organically from the interplay between matrix computations and geometry.

The R files are extra and freely available. They include basic code and templates for many of the in-text examples, most of the projects, and solutions to selected exercises. As much as possible, data sets and matrix entries are included in the files, thus reducing the amount of manual data entry required. 

Authors and Affiliations

  • Department of Mathematics and Statistics, Villanova University, Villanova, USA

    Timothy G. Feeman

About the author

​Timothy G. Feeman is professor of mathematics, Villanova University, in Lancaster, Pennsylvania. His original area of research is the theory of operators on Hilbert spaces once described as "the field of mathematics that has the strongest interaction with the scientific and technological developments which are characteristic of the twentieth century." Since the mid- to late-1990s, his scholarly efforts have become more diversified. Professor Feeman is the author of The Mathematics of Medical Imaging, also published in the "Springer Undergraduate Texts in Mathematics and Technology" series.

Bibliographic Information

  • Book Title: Applied Linear Algebra and Matrix Methods

  • Authors: Timothy G. Feeman

  • Series Title: Springer Undergraduate Texts in Mathematics and Technology

  • DOI: https://doi.org/10.1007/978-3-031-39562-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-39561-1Published: 25 November 2023

  • Softcover ISBN: 978-3-031-39564-2Due: 26 December 2023

  • eBook ISBN: 978-3-031-39562-8Published: 24 November 2023

  • Series ISSN: 1867-5506

  • Series E-ISSN: 1867-5514

  • Edition Number: 1

  • Number of Pages: XIII, 321

  • Number of Illustrations: 42 b/w illustrations, 2 illustrations in colour

  • Topics: Linear Algebra

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