Advanced Linear Algebra
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
Reviews / Votes
From 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 ZentralblattMATH
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, 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 solutionof 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)
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Person
Dr. Roman has authored 32 books, including a number of books on mathematics, such as Introduction to the Finance of Mathematics, Coding and Information Theory, and Field Theory, published by Springer-Verlag. He has also written Modules in Mathematics, a series of 15 small books designed for the general college-level liberal arts student. Besides his books for O'Reilly, Dr. Roman has written two other computer books, both published by Springer-Verlag.