Advanced Linear Algebra (Graduate Texts In Mathematics, Vol. 135)

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ISBN : 9780387728285
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Advanced Linear Algebra (Graduate Texts In Mathematics, Vol. 135)

Advanced Linear Algebra (Graduate Texts In Mathematics, Vol. 135)

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.ReviewFrom the reviews of the first edition:"? The book is very well written and has a good set of exercises. It is a suitable choice as a graduate textbook as well as a reference book." A.A. Jafarian for ZentralblattMATHFrom 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, Zentralblatt MATH, Vol. 1085, 2006)"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, May, 2005)From the reviews of the third edition:?This is the 3rd edition of a well written graduate book on linear algebra. ? The list of references has been enlarged considerably. The book is suitable for a second course on linear algebra and/or a graduate text, as well as a reference text.? (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)"This is the 3rd edition of a well written graduate book on linear algebra. ? The book covers a wide range of topics in a moderate length and careful manner. ? The list of references has been enlarged considerably. ? is suitable for a second course on linear algebra and/or a graduate text, as well as a reference text." (A. Arvanitoyeorgos, Zentralblatt MATH, Vol. 1132 (10), 2008)From the Back CoverFor 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; considerably expanded the reference section with over a hundred

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