Matrix Analysis

by Roger A. Horn, Charles R. Johnson

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

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

662 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.