Matrix Mathematics: Theory, Facts, and Formulas - Second Edition

Dennis S. Bernstein

Published by Princeton University Press 2009

Matrix Mathematics

Theory, Facts, and Formulas - Second Edition

Dennis S. Bernstein

https://doi.org/10.1515/9781400833344

Overview
Contents

About this book

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.

Each chapter describes relevant background theory followed by specialized results. Hundreds of identities, inequalities, and matrix facts are stated clearly and rigorously with cross references, citations to the literature, and illuminating remarks. Beginning with preliminaries on sets, functions, and relations,Matrix Mathematics covers all of the major topics in matrix theory, including matrix transformations; polynomial matrices; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; vector and matrix norms; the matrix exponential and stability theory; and linear systems and control theory. Also included are 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. This significantly expanded edition of Matrix Mathematics features a wealth of new material on graphs, scalar identities and inequalities, alternative partial orderings, matrix pencils, finite groups, zeros of multivariable transfer functions, roots of polynomials, convex functions, and matrix norms.

Covers hundreds of important and useful results on matrix theory, many never before available in any book

Provides a list of symbols and a summary of conventions for easy use

Includes an extensive collection of scalar identities and inequalities

Features a detailed bibliography and author index with page references

Includes an exhaustive subject index with cross-referencing

Author / Editor information

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

Reviews

It is 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 by the author. . . . I can enthusiastically recommend it to anyone who uses matrices. The author has to be applauded for the accomplishment of putting together this impressive volume.---Helmut Lutkepohl, Image

When a matrix question is thrown my way, I will now refer my correspondents . . . to Bernstein's handbook.---Philip J. Davis, SIAM News

Anybody, regardless of level of expertise, could learn new things just by browsing. Open to a random page and start reading. The reader who seeks specific information to solve a problem may also find success here.---David S. Watkins, SIAM Review

Matrix Mathematics contains an impressive collection of definitions, relations, properties, equations, inequalities, and facts centered around matrices and their use in systems and control. The amount of material that is covered is quite impressive and well structured. . . . I highly recommend the book as a source for retrieving matrix results that one would otherwise have to search for in the extensive literature on matrix theory.---Paul Van Dooren, IEEE Control Systems Magazine

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!

The book is a well-organized treasure trove of information for anyone interested in matrices and their applications. Look through the Table of Contents and see if there isn't some section that will tempt you and/or illuminate your pathway through the extensive literature on matrix theory. Researchers should have access to this authoritative and comprehensive volume. Academic and industrial libraries should have it in their reference collections. Their patrons will be grateful.---Henry Ricardo, MAA Reviews

Topics

Frontmatter Publicly Available Download PDF	i
Contents Publicly Available Download PDF	ix
Preface to the Second Edition Requires Authentication Unlicensed Licensed Download PDF	xv
Preface to the First Edition Requires Authentication Unlicensed Licensed Download PDF	xvii
Special Symbols Requires Authentication Unlicensed Licensed Download PDF	xxi
Conventions, Notation, and Terminology Requires Authentication Unlicensed Licensed Download PDF	xxxiii
Chapter One. Preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
Chapter Two. Basic Matrix Properties Requires Authentication Unlicensed Licensed Download PDF	85
Chapter Three Matrix Classes and Transformations Requires Authentication Unlicensed Licensed Download PDF	179
Chapter Four. Polynomial Matrices and Rational Transfer Functions Requires Authentication Unlicensed Licensed Download PDF	253
Chapter Five. Matrix Decompositions Requires Authentication Unlicensed Licensed Download PDF	309
Chapter Six. Generalized Inverses Requires Authentication Unlicensed Licensed Download PDF	397
Chapter Seven. Kronecker and Schur Algebra Requires Authentication Unlicensed Licensed Download PDF	439
Chapter Eight. Positive-Semidefinite Matrices Requires Authentication Unlicensed Licensed Download PDF	459
Chapter Nine. Norms Requires Authentication Unlicensed Licensed Download PDF	597
Chapter Ten. Functions of Matrices and Their Derivatives Requires Authentication Unlicensed Licensed Download PDF	681
Chapter Eleven. The Matrix Exponential and Stability Theory Requires Authentication Unlicensed Licensed Download PDF	707
Chapter Twelve. Linear Systems and Control Theory Requires Authentication Unlicensed Licensed Download PDF	795
Bibliography Requires Authentication Unlicensed Licensed Download PDF	881
Author Index Requires Authentication Unlicensed Licensed Download PDF	967
Index Requires Authentication Unlicensed Licensed Download PDF	979

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