Matrix Theory

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.

Updated and revised edition Includes a new chapter on matrix inequalities, and a new chapter with updated material on numerical ranges and radii and matrix norms Includes more than 1000 exercises Aids the reader in mastering basic matrix results and techniques that are useful for applications in various fields such as mathematics, statistics, physics, computer science, and engineering

Auteur
Fuzhen Zhang is currently a Professor of Mathematics at Nova Southeastern University.

Contenu
Preface to the Second Edition.- Preface.- Frequently Used Notation and Terminology.- Frequently Used Terms.- 1 Elementary Linear Algebra Review.- 2 Partitioned Matrices, Rank, and Eigenvalues.- 3 Matrix Polynomials and Canonical Forms.- 4 Numerical Ranges, Matrix Norms, and Special Operations.- 5 Special Types of Matrices.- 6 Unitary Matrices and Contractions.- 7 Positive Semidefinite Matrices.- 8 Hermitian Matrices.- 9 Normal Matrices.- 10 Majorization and Matrix Inequalities.- References.- Notation.- Index.