Advanced Linear Algebra
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Advanced Linear Algebra

Advanced Linear Algebra

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International Edition


About the Book

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

Table of Contents:
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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Product Details
  • ISBN-13: 9780387728285
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Edition: Revised edition
  • Language: English
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 0387728287
  • Publisher Date: 08 Oct 2007
  • Binding: Hardback
  • Height: 235 mm
  • No of Pages: 525
  • Returnable: Y


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Advanced Linear Algebra
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