Advanced Linear Algebra

Name: Advanced Linear Algebra
Availability: InStock
ISBN: 9780387728285

ISBN-10: 0387728287

ISBN-13: 9780387728285

Edition: 3rd 2008

Authors: Steven Roman

List price: $74.95

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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…

Book details

List price: $74.95
Edition: 3rd
Copyright year: 2008
Publisher: Springer New York
Publication date: 10/8/2007
Binding: Hardcover
Pages: 525
Size: 6.10" wide x 9.25" long x 1.00" tall
Weight: 2.310
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