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.
