Advanced Linear Algebra

ISBN-10: 0387728287

ISBN-13: 9780387728285

Edition: 3rd 2008

Authors: Steven Roman

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Description:

For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; corrected all known errors; the reference section has been enlarged considerably, with over a hundred references to books on linear algebra. From the reviews of the second edition: In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials. As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields. the exercises are rewritten and expanded. Overall, I found the book a very useful one. It is a suitable choice as a graduate text or as a reference book. Ali-Akbar Jafarian, ZentralblattMATH This is a formidable volume, a compendium of linear algebra theory, classical and modern . The development of the subject is elegant . The proofs are neat . The exercise sets are good, with occasional hints given for the solution of trickier problems. It represents linear algebra and does so comprehensively. Henry Ricardo, MathDL
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Book details

List price: $74.95
Edition: 3rd
Copyright year: 2008
Publisher: Springer
Publication date: 10/8/2007
Binding: Hardcover
Pages: 526
Size: 6.00" wide x 9.25" long x 1.00" tall
Weight: 1.892
Language: English

Steven Roman, Ph.D., is a professor emeritus of mathematics at the California State University, Fullerton. His previous books with O'Reilly include "Access Database Design and Programming", "Writing Excel Macros with VBA", and "Win32 API Programming with Visual Basic".

Basic Linear Algebra
Vector Spaces
Linear Transformations
The Isomorphism Theorems
Modules I: Basic Properties
Modules II: Free and Noetherian Modules
Modules over a Principal Ideal Domain
The Structure of a Linear Operator
Eigenvalues and Eigenvectors
Real and Complex Inner Product Spaces
Structure Theory for Normal Operators
Topics
Metric Vector Spaces: The Theory of Bilinear Forms
Metric Spaces
Hilbert Spaces
Tensor Products
Positive Solutions to Linear Systems: Convexity and Separation
Affine Geometry
Singular Values and the Moore-Penrose Inverse
An Introduction to Algebras
The Umbral Calculus
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