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Advanced Linear Algebra~tqw~ darksiderg

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Advanced Linear Algebra
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Type.................: Ebook
Part Size............: 2,315,362 bytes




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Posted by............: ~tqw~

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Release Notes
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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 important applications.

Table of Contents
Ch. 0 Preliminaries 1
Pt. 1 Preliminaries
Pt. 2 Algebraic Structures
Pt. 1 Basic Linear Algebra
Ch. 1 Vector Spaces 27
Ch. 2 Linear Transformations 45
Ch. 3 The Isomorphism Theorems 63
Ch. 4 Modules I 83
Ch. 5 Modules II 97
Ch. 6 Modules over Principal Ideal Domains 107
Ch. 7 The Structure of a Linear Operator 121
Ch. 8 Eigenvalues and Eigenvectors 135
Ch. 9 Real and Complex Inner Product Spaces 157
Ch. 10 The Spectral Theorem for Normal Operators 175
Pt. 2 Topics
Ch. 11 Metric Vector Spaces 205
Ch. 12 Metric Spaces 239
Ch. 13 Hilbert Spaces 263
Ch. 14 Tensor Products 291
Ch. 15 Affine Geometry 315
Ch. 16 The Umbral Calculus 329
References 353
Index of Notation 355
Index 357

Product Details

* ISBN: 0387728287
* ISBN-13: 9780387728285
* Format: Hardcover
* Publisher: Springer-Verlag New York, LLC
* Pub. Date: October 2007

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