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Advanced Linear Algebra<br />
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General Information<br />
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Type.................: Ebook<br />
Part Size............: 2,315,362 bytes<br />
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Posted by............: ~tqw~<br />
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Release Notes<br />
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This is a graduate textbook covering an especially broad range of topics. The <br />
first part of the book contains a careful but rapid discussion of the basics of <br />
linear algebra, including vector spaces, linear transformations, quotient <br />
spaces, and isomorphism theorems. The author then proceeds to modules, <br />
emphasizing a comparison with vector spaces. A thorough discussion of inner <br />
product spaces, eigenvalues, eigenvectors, and finite dimensional spectral <br />
theory follows, culminating in the finite dimensional spectral theorem for <br />
normal operators. The second part of the book is a collection of topics, <br />
including metric vector spaces, metric spaces, Hilbert spaces, tensor products, <br />
and affine geometry. The last chapter discusses the umbral calculus, an area of <br />
modern algebra with important applications.<br />
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Table of Contents<br />
Ch. 0 Preliminaries 1<br />
Pt. 1 Preliminaries <br />
Pt. 2 Algebraic Structures <br />
Pt. 1 Basic Linear Algebra <br />
Ch. 1 Vector Spaces 27<br />
Ch. 2 Linear Transformations 45<br />
Ch. 3 The Isomorphism Theorems 63<br />
Ch. 4 Modules I 83<br />
Ch. 5 Modules II 97<br />
Ch. 6 Modules over Principal Ideal Domains 107<br />
Ch. 7 The Structure of a Linear Operator 121<br />
Ch. 8 Eigenvalues and Eigenvectors 135<br />
Ch. 9 Real and Complex Inner Product Spaces 157<br />
Ch. 10 The Spectral Theorem for Normal Operators 175<br />
Pt. 2 Topics <br />
Ch. 11 Metric Vector Spaces 205<br />
Ch. 12 Metric Spaces 239<br />
Ch. 13 Hilbert Spaces 263<br />
Ch. 14 Tensor Products 291<br />
Ch. 15 Affine Geometry 315<br />
Ch. 16 The Umbral Calculus 329<br />
References 353<br />
Index of Notation 355<br />
Index 357<br />
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Product Details<br />
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* ISBN: 0387728287<br />
* ISBN-13: 9780387728285<br />
* Format: Hardcover<br />
* Publisher: Springer-Verlag New York, LLC<br />
* Pub. Date: October 2007<br />
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