Matrix Mathematics: Theory, Facts, and Formulas (Second Edition)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 easytouse 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; positivesemidefinite 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.

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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 
Other editions  View all
Matrix Mathematics: Theory, Facts, and Formulas, Second Edition Dennis S. Bernstein Limited preview  2009 
Matrix Mathematics: Theory, Facts, and Formulas (Second Edition) Dennis S. Bernstein No preview available  2009 