Advanced linear algebra
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, e...
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2017
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oai:112.137.131.14:VNU_123-240742020-06-21T04:38:42Z Advanced linear algebra Roman, Steven. Mathematics Vector Spaces ; Algebras, Linear 512.5 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. 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 2017-04-04T04:26:35Z 2017-04-04T04:26:35Z 2008 Book 978-0-387-72828-5 978-0-387-72831-5 http://repository.vnu.edu.vn/handle/VNU_123/24074 en ©2008 Springer Science+Business Media, LLC Linear algebra 528 p. application/pdf Springer |
| institution |
Vietnam National University, Hanoi |
| building |
VNU Library & Information Center |
| country |
Vietnam |
| collection |
VNU Digital Repository |
| language |
English |
| topic |
Mathematics Vector Spaces ; Algebras, Linear 512.5 |
| spellingShingle |
Mathematics Vector Spaces ; Algebras, Linear 512.5 Roman, Steven. Advanced linear algebra |
| description |
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. |
| format |
Book |
| author |
Roman, Steven. |
| author_facet |
Roman, Steven. |
| author_sort |
Roman, Steven. |
| title |
Advanced linear algebra |
| title_short |
Advanced linear algebra |
| title_full |
Advanced linear algebra |
| title_fullStr |
Advanced linear algebra |
| title_full_unstemmed |
Advanced linear algebra |
| title_sort |
advanced linear algebra |
| publisher |
Springer |
| publishDate |
2017 |
| url |
http://repository.vnu.edu.vn/handle/VNU_123/24074 |
| _version_ |
1680963450545635328 |