Advanced Linear Algebra / by Steven Roman
(Graduate Texts in Mathematics ; 135)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | New York, NY : Springer New York |
| 出版年 | 2005 |
| 本文言語 | 英語 |
| 大きさ | XVI, 486 p. 18 illus : online resource |
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| 内容注記 | 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 |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Roman, Steven author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Matrix theory LCSH:Algebra FREE:Mathematics FREE:Linear and Multilinear Algebras, Matrix Theory |
| 分 類 | DC23:512.5 |
| 巻冊次 | ISBN:9780387274744 
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| ISBN | 9780387274744 |
| URL | http://dx.doi.org/10.1007/0-387-27474-X |
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