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140122 ||| eng |
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|a 9781475721782
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| 100 |
1 |
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|a Roman, Steven
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| 245 |
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|a Advanced Linear Algebra
|h Elektronische Ressource
|c by Steven Roman
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| 250 |
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|a 1st ed. 1992
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| 260 |
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|a New York, NY
|b Springer New York
|c 1992, 1992
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| 300 |
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|a XII, 370 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Linear Algebra
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| 653 |
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|a Algebras, Linear
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Graduate Texts in Mathematics
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| 028 |
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|a 10.1007/978-1-4757-2178-2
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| 856 |
4 |
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|u https://doi.org/10.1007/978-1-4757-2178-2?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 512.5
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| 520 |
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|a 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
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