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008			090221s2005 nyua |b 001 0 eng
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050	0	0	_aQA184.2 _b.R66 2005
082	0	0	_a512/.5 _222
100	1		_aRoman, Steven. _949794
245	1	0	_aAdvanced Linear Algebra / _cSteven Roman.
250			_a2nd ed.
260			_aNew York : _bSpringer, _cc2005.
300			_axvi, 482 p. : _bill. ; _c25 cm.
440		0	_aGraduate texts in mathematics ; _v135 _91563
504			_aIncludes bibliographical references (p. [473]-474) and index.
505			_aVector Spaces.- Linear Transformations.- The Isomorphism Theorems.- Modules I: Basic Properties.- Modules II: Free and Noetherian Modules.- Modules over a Principal Ideal Domain.- The Structure of a Linear Operator.- Eigenvalues and Eigenvectors.- Real and Complex Inner Product Spaces.- Structure Theory for Normal Operators.- Metric Vector Spaces: The Theory of Bilinear Forms.- Metric Spaces.- Hilbert Spaces.- Tensor Products.- Positive Solutions to Linear Systems: Convexity and Separation.- Affine Geometry.- Operator Factorizations: QR and Singular Value.- The Umbral Calculus.- References.- Index.
520			_aThis 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.The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.
650		0	_aAlgebras, Linear. _91024
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/enhancements/fy0662/2005040244-d.html
942			_2lcc _n0 _cBK
999			_c23653 _d23653