 Contains topics that are not generally found in linear algebra books
 Offers especially broad coverage
 Provides encyclopedic treatment of linear algebra theory, both classical and modern
 An extensive bibliography has been added in this new edition
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 About this Textbook

For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finitedimensional 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 finitedimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section 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."
AliAkbar 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, MAA Online
 About the authors

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 SpringerVerlag. He has also written Modules in Mathematics, a series of 15 small books designed for the general collegelevel liberal arts student. Besides his books for O'Reilly, Dr. Roman has written two other computer books, both published by SpringerVerlag.
 Reviews

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." (AliAkbar 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)
 Table of contents (19 chapters)


Vector Spaces
Pages 3558

Linear Transformations
Pages 5985

The Isomorphism Theorems
Pages 87107

Modules I: Basic Properties
Pages 109126

Modules II: Free and Noetherian Modules
Pages 127138

Table of contents (19 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Advanced Linear Algebra
 Authors

 Steven Roman
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 135
 Copyright
 2008
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387728315
 DOI
 10.1007/9780387728315
 Hardcover ISBN
 9780387728285
 Softcover ISBN
 9781441924988
 Series ISSN
 00725285
 Edition Number
 3
 Number of Pages
 XVIII, 525
 Topics
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