Advanced Linear Algebra~tqw~ darksiderg

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  Advanced Linear Algebra~tqw~ darksiderg
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• Size:
  2.2 MB
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• Added:
  05/15/2008
• Last check:
  2009-06-09 08:55:24
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  *******************************************************************************<br /> Advanced Linear Algebra<br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 2,315,362 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> 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 /> <br /> 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 /> <br /> Product Details<br /> <br /> * ISBN: 0387728287<br /> * ISBN-13: 9780387728285<br /> * Format: Hardcover<br /> * Publisher: Springer-Verlag New York, LLC<br /> * Pub. Date: October 2007<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> Adobe Acrobet Reader
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