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Advanced Linear Algebra ******************************************************************************* General InformationType.................: Ebook Part Size............: 2,315,362 bytes Post InformationPosted by............: ~tqw~ Release NotesThis 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 Install NotesAdobe Acrobet Reader Sharing Widget |