# Advanced Linear Algebra

- 76 Citations
- 1 Mentions
- 225k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 135)

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Textbook

- 76 Citations
- 1 Mentions
- 225k Downloads

Part of the Graduate Texts in Mathematics book series (GTM, volume 135)

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; 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."

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, MAA Online

Eigenvalue Eigenvector algebra field linear algebra transformation

- DOI https://doi.org/10.1007/978-0-387-72831-5
- Copyright Information Springer-Verlag New York 2008
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-0-387-72828-5
- Online ISBN 978-0-387-72831-5
- Series Print ISSN 0072-5285
- Series Online ISSN 2197-5612
- Buy this book on publisher's site