Matrix Analysis

by Roger A. Horn, Charles R. Johnson

Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.

Genres: Mathematics, Textbooks, Reference, Science, Algebra, Technical

575 pages, Paperback

First published December 27, 1985

Reviews

[Laura Pascalache · Rating 5 out of 5]

Excellent book, I read it before a Math contest and not only did it help me remember and explore deep matrix analysis areas but it also had thorough proofs and ideas that are applicable in many problems.
I strongly recommend it!

[Nolan · Rating 5 out of 5]

The de facto starting point for upper undergraduate/graduate level linear algebra. The first chapter (zeroth chapter?) provides a quick recap of basic linear algebra and the remainder of the book dives deeper into fundamental results in matrix theory.

The subject matter of the text includes
- Matrix decompositions
- Major results on every common family of matrix (nonnegative, primitive, normal, unitary, hermitian, definite/semidefine)
- Normal and canonical matrix forms
- The eigenvalue/eigenvector problem
- Operator norms
- Perturbation

This text boasts over 42000 citations in various journals of linear algebra, and for good reason. A must-have for any serious matrix theorist.

[Matthew Morgan · Rating 4 out of 5]

A comprehensive resource on an important subject for my work.

[Julie · Rating 3 out of 5]

This book is very thorough, but dense. It's a nice reference to have on hand.