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Matrix Theory

Basic Results and Techniques

  • Fuzhen┬áZhang

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Fuzhen Zhang
    Pages 1-34
  3. Fuzhen Zhang
    Pages 73-106
  4. Fuzhen Zhang
    Pages 125-170
  5. Fuzhen Zhang
    Pages 171-198
  6. Fuzhen Zhang
    Pages 199-252
  7. Fuzhen Zhang
    Pages 253-292
  8. Fuzhen Zhang
    Pages 293-324
  9. Fuzhen Zhang
    Pages 325-378
  10. Back Matter
    Pages 379-399

About this book

Introduction

The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems.

Major changes in this revised and expanded second edition:
-Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms
-The inclusion of more than 1000 exercises
-A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices
-A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms.

This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. Prerequisites include a decent background in elementary linear algebra and calculus. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields.

Fuzhen Zhang is a professor of mathematics at Nova Southeastern University, Fort Lauderdale, Florida. He received his Ph.D. in Mathematics from the University of California at Santa Barbara, M.S. from Beijing Normal University, and B.Sc. from Shenyang Normal University (China). In addition to research papers, he is the author of the book Linear Algebra: Challenging Problems for Students and the editor of The Schur Complement and Its Applications.

Keywords

Hermitian matrices compound matrices contractions linear algebra majorization inequalities matrix decompositions matrix functions matrix inequalities matrix polynomials matrix theory normal matrices partitioned matrices positive semidefinite matrices unitary matrices

Authors and affiliations

  • Fuzhen┬áZhang
    • 1
  1. 1.Dept. of MathematicsNova Southeastern UniversityFort LauderdaleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1099-7
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1098-0
  • Online ISBN 978-1-4614-1099-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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