Cover; Title Page; Copyright Page; Dedication; Contents; Preface to the Revised and Expanded Edition; Preface to the Second Edition; Preface to the First Edition; Special Symbols; Conventions, Notation, and Terminology; 1. Sets, Logic, Numbers, Relations, Orderings, Graphs, and Functions; 1.1 Sets; 1.2 Logic; 1.3 Relations and Orderings; 1.4 Directed and Symmetric Graphs; 1.5 Numbers; 1.6 Functions and Their Inverses; 1.7 Facts on Logic; 1.8 Facts on Sets; 1.9 Facts on Graphs; 1.10 Facts on Functions; 1.11 Facts on Integers; 1.12 Facts on Finite Sums; 1.13 Facts on Factorials. 1.14 Facts on Finite Products1.15 Facts on Numbers; 1.16 Facts on Binomial Coefficients; 1.17 Facts on Fibonacci, Lucas, and Pell Numbers; 1.18 Facts on Arrangement, Derangement, and Catalan Numbers; 1.19 Facts on Cycle, Subset, Eulerian, Bell, and Ordered Bell Numbers; 1.20 Facts on Partition Numbers, the Totient Function, and Divisor Sums; 1.21 Facts on Convex Functions; 1.22 Notes; 2. Equalities and Inequalities; 2.1 Facts on Equalities and Inequalities in One Variable; 2.2 Facts on Equalities and Inequalities in Two Variables; 2.3 Facts on Equalities and Inequalities in Three Variables. 2.4 Facts on Equalities and Inequalities in Four Variables2.5 Facts on Equalities and Inequalities in Five Variables; 2.6 Facts on Equalities and Inequalities in Six Variables; 2.7 Facts on Equalities and Inequalities in Seven Variables; 2.8 Facts on Equalities and Inequalities in Eight Variables; 2.9 Facts on Equalities and Inequalities in Nine Variables; 2.10 Facts on Equalities and Inequalities in Sixteen Variables; 2.11 Facts on Equalities and Inequalities in n Variables; 2.12 Facts on Equalities and Inequalities in 2n Variables; 2.13 Facts on Equalities and Inequalities in 3n Variables. 2.14 Facts on Equalities and Inequalities in 4n Variables2.15 Facts on Equalities and Inequalities for the Logarithm Function; 2.16 Facts on Equalities for Trigonometric Functions; 2.17 Facts on Inequalities for Trigonometric Functions; 2.18 Facts on Equalities and Inequalities for Inverse Trigonometric Functions; 2.19 Facts on Equalities and Inequalities for Hyperbolic Functions; 2.20 Facts on Equalities and Inequalities for Inverse Hyperbolic Functions; 2.21 Facts on Equalities and Inequalities in Complex Variables; 2.22 Notes; 3. Basic Matrix Properties; 3.1 Vectors; 3.2 Matrices. 3.3 Transpose and Inner Product3.4 Geometrically Defined Sets; 3.5 Range and Null Space; 3.6 Rank and Defect; 3.7 Invertibility; 3.8 The Determinant; 3.9 Partitioned Matrices; 3.10 Majorization; 3.11 Facts on One Set; 3.12 Facts on Two or More Sets; 3.13 Facts on Range, Null Space, Rank, and Defect; 3.14 Facts on the Range, Rank, Null Space, and Defect of Partitioned Matrices; 3.15 Facts on the Inner Product, Outer Product, Trace, and Matrix Powers; 3.16 Facts on the Determinant; 3.17 Facts on the Determinant of Partitioned Matrices; 3.18 Facts on Left and Right Inverses

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