Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas - Revised and Expanded Edition

Description

The essential reference book on matrices--now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. * Fully updated and expanded with new material on scalar and vector mathematics* Covers the latest results in matrix theory* Provides a list of symbols and a summary of conventions for easy and precise use* Includes an extensive bibliography with back-referencing plus an author index

Dennis S. Bernstein is professor of aerospace engineering at the University of Michigan.

Praise for the previous editions: "When a matrix question is thrown my way, I will now refer my correspondents ... to Bernstein's handbook."--Philip J. Davis, SIAM News Praise for the previous editions: "The amount of material that is covered is quite impressive and well structured... I highly recommend the book as a source for retrieving or verifying matrix results that one would otherwise have to search for in the extensive literature on matrix theory."--Paul Van Dooren, IEEE Control Systems Magazine Praise for the previous editions: "The author was very successful in collecting the enormous amount of results in matrix theory in a single source... A beautiful work and an admirable performance!"--Monatshefte fur Mathematik Praise for the previous editions: "A remarkable source of matrix results. I will put it on the shelf near to my desk so that I have quick access to it. The book is an impressive accomplishment."--Helmut Lutkepohl, Image Praise for the previous editions: "A well-organized treasure trove of information for anyone interested in matrices and their applications."--Henry Ricardo, MAA Reviews