Scalar, Vector, and Matrix Mathematics
eBook - PDF

Scalar, Vector, and Matrix Mathematics

Theory, Facts, and Formulas - Revised and Expanded Edition

  1. 1,600 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Scalar, Vector, and Matrix Mathematics

Theory, Facts, and Formulas - Revised and Expanded Edition

About this book

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

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Yes, you can access Scalar, Vector, and Matrix Mathematics by Dennis S. Bernstein in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Dedication
  5. Contents
  6. Preface to the Revised and Expanded Edition
  7. Preface to the Second Edition
  8. Preface to the First Edition
  9. Special Symbols
  10. Conventions, Notation, and Terminology
  11. 1. Sets, Logic, Numbers, Relations, Orderings, Graphs, and Functions
  12. 2. Equalities and Inequalities
  13. 3. Basic Matrix Properties
  14. 4. Matrix Classes and Transformations
  15. 5. Geometry
  16. 6. Polynomial Matrices and Rational Transfer Functions
  17. 7. Matrix Decompositions
  18. 8. Generalized Inverses
  19. 9. Kronecker and Schur Algebra
  20. 10. Positive-Semidefinite Matrices
  21. 11. Norms
  22. 12. Functions, Limits, Sequences, Series, Infinite Products, and Derivatives
  23. 13. Infinite Series, Infinite Products, and Special Functions
  24. 14. Integrals
  25. 15. The Matrix Exponential and Stability Theory
  26. 16. Linear Systems and Control Theory
  27. Bibliography
  28. Author Index
  29. Subject Index