Ebook Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, by Dennis S. Bernstein
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Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, by Dennis S. Bernstein
Ebook Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, by Dennis S. Bernstein
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Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application.
Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory.
A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.
- Sales Rank: #3008506 in Books
- Brand: Brand: Princeton University Press
- Published on: 2005-03-14
- Original language: English
- Number of items: 1
- Dimensions: 1.50" h x 7.22" w x 10.14" l,
- Binding: Hardcover
- 768 pages
- Used Book in Good Condition
Review
"When a matrix question is thrown my way, I will now refer my correspondents . . . to Bernstein's handbook."--Philip J. Davis, SIAM News
"Matrix Mathematics contains an impressive collection of definitions, relations, properties, equations, inequalities, and facts centered around matrices and their use in systems and control. The amount of material that is covered is quite impressive and well structured. . . . I highly recommend the book as a source for retrieving matrix results that one would otherwise have to search for in the extensive literature on matrix theory."--Paul Van Dooren, IEEE Control Systems Magazine
"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
About the Author
Dennis S. Bernstein is a Professor of Aerospace Engineering at the University of Michigan.
Most helpful customer reviews
6 of 6 people found the following review helpful.
At Last!
By ScienceOfSleep
This book will become a classic... Like other reviewers, I have copies of many of the important works on matrix theory, but, for example- Needed a result on simultaneous diagonalization. Where to find it? In "Introduction to Statistical Pattern Recognition", Fukunaga, or do it from scratch, or... in this text, along with pretty much every other result that I could want. So, I'm buying a copy both for its completeness and organization. It'll be the first stop every time I'm scratching my head over a matrix algebra problem. Thanks to Bernstein for making my life a bit easier.
20 of 22 people found the following review helpful.
Where do you find that arcane result ?
By Flavio Cipparrone
Sometimes it is very difficult to find out a matrix theorem that is used in a technical publication.
I have books by Gantmacher, Horn, Meyer (undergraduate), Kunze and Hoffman and Jan Magnus but if you NEED to quickly find a result, open this book. Thousands of matrix theorems and facts.
Very good reference.
3 of 5 people found the following review helpful.
Great book
By Michael Margaliot
I found this to be an extremely useful book. Its internal organization, extensive index and tables of symbols make it very easy to find exactly the result you need.
I strongly recommend this book to people working in applied mathematics or engineering.
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