Matrix Mathematics: Theory, Facts, and Formulas (Second Edition)

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Princeton University Press, Jul 26, 2009 - Mathematics - 1139 pages
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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

 

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Contents

Preliminaries
1
Basic Matrix Properties
85
Matrix Classes and Transformations
179
Polynomial Matrices and Rational Transfer Functions
253
Matrix Decompositions
309
Generalized Inverses
397
Kronecker and Schur Algebra
439
PositiveSemidefinite Matrices
459
Norms
597
Functions of Matrices and Their Derivatives
681
The Matrix Exponential and Stability Theory
707
Linear Systems and Control Theory
795
Bibliography
881
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About the author (2009)

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

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