Scalar, Vector, And Matrix Mathematics: Theory, Facts, And Formulas

Description

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. Cover......Page 1 Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas......Page 5 Copyright......Page 6 Dedication......Page 7 Contents ......Page 11 Preface to the Revised and Expanded Edition......Page 19 Preface to the Second Edition......Page 21 Preface to the First Edition......Page 23 Special Symbols......Page 27 Conventions, Notation, and Terminology......Page 39 1 Sets, Logic, Numbers, Relations, Orderings, Graphs, and Functions......Page 49 2 Equalities and Inequalities......Page 167 3 Basic Matrix Properties......Page 325 4 Matrix Classes and Transformations......Page 411 5 Geometry......Page 489 6 Polynomial Matrices and Rational Transfer Functions......Page 547 7 Matrix Decompositions......Page 593 8 Generalized Inverses......Page 669 9 Kronecker and Schur Algebra......Page 729 10 Positive-Semidefinite Matrices......Page 751 11 Norms......Page 881 12 Functions, Limits, Sequences, Series, Infinite Products, and Derivatives......Page 961 13 Infinite Series, Infinite Products, and Special Functions......Page 1023 14 Integrals......Page 1141 15 The Matrix Exponential and Stability Theory......Page 1227 16 Linear Systems and Control Theory......Page 1297 Bibliography......Page 1369 Author Index......Page 1481 Index......Page 1497