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Introduction to Matrix Theory

  • Textbook
  • © 2021

Overview

Authors:
  1. Arindama Singh

    1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

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  • Covers topics such as elementary row operations and Gram–Schmidt orthogonalization, rank factorization, OR-factorization, Schurtriangularization, diagonalization of normal matrices, etc
  • Includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix
  • Contains exercises and problems at the end of each chapter

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Matrix Operations

    • Arindama Singh
    Pages 1-30

  3. Systems of Linear Equations

    • Arindama Singh
    Pages 31-52

  4. Matrix as a Linear Map

    • Arindama Singh
    Pages 53-80

  5. Orthogonality

    • Arindama Singh
    Pages 81-99

  6. Eigenvalues and Eigenvectors

    • Arindama Singh
    Pages 101-113

  7. Canonical Forms

    • Arindama Singh
    Pages 115-156

  8. Norms of Matrices

    • Arindama Singh
    Pages 157-187

  9. Back Matter

    Pages 189-194
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Keywords

About this book

This book is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

Reviews

“This is a concise, concrete introduction to matrix theory and linear algebra, designed as a one-semester course for science and engineering students. … The book has a reasonable number of exercises.” (Allen Stenger, MAA Reviews, December 12, 2021)

Authors and Affiliations

  • Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Arindama Singh

About the author

Dr. Arindama Singh is a professor in the Department of Mathematics, Indian Institute of Technology (IIT) Madras, India. He received his Ph.D. degree from the IIT Kanpur, India, in 1990. His research interests include knowledge compilation, singular perturbation, mathematical learning theory, image processing, and numerical linear algebra. He has published six books, over 60 papers in journals and conferences of international repute. He has guided five Ph.D. students and is a life member of many academic bodies, including the Indian Society for Industrial and Applied Mathematics, Indian Society of Technical Education, Ramanujan Mathematical Society, Indian Mathematical Society, and The Association of Mathematics Teachers of India.

Bibliographic Information

  • Book Title: Introduction to Matrix Theory

  • Authors: Arindama Singh

  • DOI: https://doi.org/10.1007/978-3-030-80481-7

  • 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 2021

  • Hardcover ISBN: 978-3-030-80480-0Published: 17 August 2021

  • Softcover ISBN: 978-3-030-80483-1Published: 18 August 2022

  • eBook ISBN: 978-3-030-80481-7Published: 16 August 2021

  • Edition Number: 1

  • Number of Pages: IX, 194

  • Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour

  • Topics: Linear Algebra, Engineering Mathematics, Mathematical Physics

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