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

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9780691151205: Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas

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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From the Back Cover:

"This book contains a huge variety of results on matrix and linear algebra, painstakingly collected from numerous sources. Having already become a main reference for anyone interested in the theory and practice of matrices, this new edition includes a wealth of additional material. If you have any questions about sets, graphs, and functions, derivatives and integrals, sequences and limits, and even geometry, you will almost certainly find an answer here."--Götz Trenkler, Technical University of Dortmund, Germany

"Bernstein's book inherits each and every virtue of its valued predecessors and offers much more than just updating. New topics have been covered and many novel results included, and the author has made a tremendous effort to present them in a clear, concise, and logical way. This book will remain the primary reference for engineers, mathematicians, physicists, statisticians, and other scientists interested in pure and applied matrix analysis and related topics."--Oskar Baksalary, Adam Mickiewicz University, Poznan, Poland

"Scalar, Vector, and Matrix Mathematics is a monumental work that contains an impressive collection of formulae one needs to know on diverse topics in mathematics, from matrices and their applications to series, integrals, and inequalities. The bibliography is vast and well documented, and the presentation is appealing and accessible."--Ovidiu Furdui, Technical University of Cluj-Napoca, Romania

"This is a book that any mathematician, physicist, or engineer would want to have at hand. If you are looking for a particular mathematical identity, an inequality, or a fact about matrices, then it is most likely that you will find it in this encyclopedic work."--Omran Kouba, Higher Institute for Applied Sciences and Technology, Damascus

About the Author:

Dennis S. Bernstein is professor of aerospace engineering at the University of Michigan.

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