# Matrix Theory

## Basic Results and Techniques

• Fuzhen Zhang
Textbook

Part of the Universitext book series (UTX)

1. Front Matter
Pages i-xvii
2. Fuzhen Zhang
Pages 1-34
3. Fuzhen Zhang
Pages 35-72
4. Fuzhen Zhang
Pages 73-106
5. Fuzhen Zhang
Pages 107-124
6. Fuzhen Zhang
Pages 125-170
7. Fuzhen Zhang
Pages 171-198
8. Fuzhen Zhang
Pages 199-252
9. Fuzhen Zhang
Pages 253-292
10. Fuzhen Zhang
Pages 293-324
11. Fuzhen Zhang
Pages 325-378
12. Back Matter
Pages 379-399

### 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 Zhang
• 1
1. 1.Dept. of MathematicsNova Southeastern UniversityFort LauderdaleUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4614-1099-7