Although this 1400-page book stretches the meaning of ‘handbook’ to its breaking point, it is a valuable compendium of information on virtually all aspects of linear algebra and its applications. A similar, but less comprehensive book is Matrix Mathematics by Dennis S. Bernstein, a useful reference work motivated by the utility of “matrix facts” in science, mathematics, and engineering problems.

The book’s 77 chapters are divided into five broad categories: Basic linear algebra, combinatorial matrix theory and graphs, numerical methods, applications, and computational software. There are also six pages of preliminary definitions. Each chapter, written by an expert or team of experts, follows the same basic format: Definitions, Facts, Examples, and References. There are frequent cross references between chapters and sections. The book concludes with a 40-page cross-referenced Glossary, a 9-page Notation Index, and a 56-page Index, beginning with “Abelian, Lie algebras” and ending with “Zyskind-Martin model.” A half-page errata list (as of 3/1/07) and two “additional useful facts” for Section 2.4 are available online.

Unlike the classic two-volume work by Horn and Johnson, this book contains no proofs, but the authors have been encouraged to use standard texts or survey articles as references whenever possible; and most end-of-chapter lists also include reasonably current research articles/reports. (The latest references I caught in my perambulations through this book were a research report published in 2006 and several papers submitted for publication.)

This is a Herculean labor of love on the editor’s part, a successful effort that should be appreciated and applauded by anyone working and/or teaching in this important area of mathematics. Although it is possible that a reader may find some favorite piece of information missing — I couldn’t find the evaluation of a determinant via the *PA* = *LU* decomposition, for example — most users of this volume will be pleased at its thoroughness. Every library that supports mathematics and science departments should have this encyclopedic work on its shelves

Henry Ricardo ([email protected]) is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book *A Modern Introduction to Differential Equations* was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.