 Contains topics that are not generally found in linear algebra books
 Coverage is especially broad
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 About this Textbook

This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications.
The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added.
The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance.
 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)
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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
 2005
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387274744
 DOI
 10.1007/038727474X
 Series ISSN
 00725285
 Edition Number
 2
 Number of Pages
 XVI, 486
 Number of Illustrations and Tables
 18 b/w illustrations
 Topics