Scalar, Vector, and Matrix Mathematics

Theory, Facts, and Formulas - Revised and Expanded Edition

Dennis S. Bernstein

• Publisher: Princeton University Press
• Year: 2018
• ISBN:
  9781400888252
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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

Table of contents

• 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
• 2. Equalities and Inequalities
• 3. Basic Matrix Properties
• 4. Matrix Classes and Transformations
• 5. Geometry
• 6. Polynomial Matrices and Rational Transfer Functions
• 7. Matrix Decompositions
• 8. Generalized Inverses
• 9. Kronecker and Schur Algebra
• 10. Positive-Semidefinite Matrices
• 11. Norms
• 12. Functions, Limits, Sequences, Series, Infinite Products, and Derivatives
• 13. Infinite Series, Infinite Products, and Special Functions
• 14. Integrals
• 15. The Matrix Exponential and Stability Theory
• 16. Linear Systems and Control Theory
• Bibliography
• Author Index
• Subject Index