Theory Of Matrices

The Theory of Matrices

Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.

The Theory of Matrices

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 eight 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. For many theorems several different proofs are given. The book can be used as a text or a supplement for a linear algebra and matrix theory class or seminar for senior or graduate students. The only prerequisites are 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.