Advanced Linear Algebra
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 module...
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| 主要作者: | |
|---|---|
| 格式: | Livre numérique |
| 語言: | Anglais |
| 出版: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| 版: | Second Edition. |
| 叢編: | Graduate Texts in Mathematics
135 |
| 在線閱讀: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 提示: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Advanced linear algebra, Steven Roman, 2e éd., New York, Springer, 2005, 1 volume (xvi, 482 pages), Graduate texts in mathematics, 0-387-24766-1 • Tracking, identification and control, proceedings, of the 1st international conference, 2-3 November 1988, London, UK, Kempston, IFS, Springer, 1988, 1 vol. (VII-206 p.), 1-85423-025-5 • Advanced linear algebra, Steven Roman, 2e éd., New York, Springer, 2005, 1 volume (xvi, 482 pages), Graduate texts in mathematics, 0-387-24766-1 |
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| 245 | 1 | 0 | |a Advanced Linear Algebra |c by Steven Roman. |
| 250 | |a Second Edition. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 135 |x 2197-5612 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Preliminaries Preliminaries Basic Linear Algebra Vector Spaces Linear Transformations The Isomorphism Theorems Modules I: Basic Properties Modules II: Free and Noetherian Modules Modules over a Principal Ideal Domain The Structure of a Linear Operator Eigenvalues and Eigenvectors Real and Complex Inner Product Spaces Structure Theory for Normal Operators Topics Metric Vector Spaces: The Theory of Bilinear Forms Metric Spaces Hilbert Spaces Tensor Products Positive Solutions to Linear Systems: Convexity and Separation Affine Geometry Operator Factorizations: QR and Singular Value The Umbral Calculus | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 776 | 0 | |0 087313006 |t Advanced linear algebra |f Steven Roman |e 2e éd. |c New York |n Springer |d 2005 |p 1 volume (xvi, 482 pages) |s Graduate texts in mathematics |z 0-387-24766-1 | |
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| 776 | 0 | |0 087313006 |t Advanced linear algebra |f Steven Roman |e 2e éd. |c New York |n Springer |d 2005 |p 1 volume (xvi, 482 pages) |s Graduate texts in mathematics |z 0-387-24766-1 | |
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