Advanced Linear Algebra / by Steven Roman
(Graduate Texts in Mathematics ; 135)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1992 |
| 本文言語 | 英語 |
| 大きさ | XII, 370 p : online resource |
書誌詳細を非表示
| 内容注記 | 0 Preliminaries 1 Vector Spaces 2 Linear Transformations 3 The Isomorphism Theorems 4 Modules I 5 Modules II 6 Modules over Principal Ideal Domains 7 The Structure of a Linear Operator 8 Eigenvalues and Eigenvectors 9 Real and Complex Inner Product Spaces 10 The Spectral Theorem for Normal Operators 11 Metric Vector Spaces 12 Metric Spaces 13 Hilbert Spaces 14 Tensor Products 15 Affine Geometry 16 The Umbral Calculus References Index of Notation |
|---|---|
| 一般注記 | This book is a thorough introduction to linear algebra, for the graduate or advanced undergraduate student. Prerequisites are limited to a knowledge of the basic properties of matrices and determinants. However, since we cover the basics of vector spaces and linear transformations rather rapidly, a prior course in linear algebra (even at the sophomore level), along with a certain measure of "mathematical maturity," is highly desirable. Chapter 0 contains a summary of certain topics in modern algebra that are required for the sequel. This chapter should be skimmed quickly and then used primarily as a reference. Chapters 1-3 contain a discussion of the basic properties of vector spaces and linear transformations. Chapter 4 is devoted to a discussion of modules, emphasizing a comparison between the properties of modules and those of vector spaces. Chapter 5 provides more on modules. The main goals of this chapter are to prove that any two bases of a free module have the same cardinality and to introduce noetherian modules. However, the instructor may simply skim over this chapter, omitting all proofs. Chapter 6 is devoted to the theory of modules over a principal ideal domain, establishing the cyclic decomposition theorem for finitely generated modules. This theorem is the key to the structure theorems for finite dimensional linear operators, discussed in Chapters 7 and 8. Chapter 9 is devoted to real and complex inner product spaces |
| 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:9781475721782 
|
| ISBN | 9781475721782 |
| URL | http://dx.doi.org/10.1007/978-1-4757-2178-2 |
目次／あらすじ