Scalar, Vector, and Matrix Mathematics - by Dennis S Bernstein

About the Book

"Revised and expanded edition of Matrix mathematics, retitled Scalar, vector, and matrix mathematics"--Preface.

Book Synopsis

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

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

Review Quotes

"Praise for the previous editions: "A remarkable source of matrix results. I will put it on the shelf near to my desk so that I have quick access to it. The book is an impressive accomplishment.""---Helmut Lütkepohl, Image

"Praise for the previous editions: "A well-organized treasure trove of information for anyone interested in matrices and their applications.""---Henry Ricardo, MAA Reviews

"Praise for the previous editions: "The amount of material that is covered is quite impressive and well structured. . . . I highly recommend the book as a source for retrieving or verifying matrix results that one would otherwise have to search for in the extensive literature on matrix theory.""---Paul Van Dooren, IEEE Control Systems Magazine

"Praise for the previous editions: "The author was very successful in collecting the enormous amount of results in matrix theory in a single source. . . . A beautiful work and an admirable performance!""-- "Monatshefte für Mathematik"

"Praise for the previous editions: "When a matrix question is thrown my way, I will now refer my correspondents . . . to Bernstein's handbook.""---Philip J. Davis, SIAM News

"This book achieves a breakthrough. . . . It is simultaneously an introductory and completely self-contained textbook for students, a handbook for researchers, a reference work, and a research monograph. . . . I am not aware of any close comparison of this book, and in the years to come, Bernstein's book will ever be on my office shelf."---Jaydeb Sarkar, Zentralblatt MATH

About the Author

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