000			03905nam a22004935i 4500
001			978-0-387-27474-4
003			DE-He213
005			20160614135109.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387274744 _9978-0-387-27474-4
024	7		_a10.1007/0-387-27474-X _2doi
049			_aAlfaisal Main Library
050		4	_aQA184-205
072		7	_aPBF _2bicssc
072		7	_aMAT002050 _2bisacsh
082	0	4	_a512.5 _223
100	1		_aRoman, Steven. _eauthor.
245	1	0	_aAdvanced Linear Algebra _h[electronic resource] / _cby Steven Roman.
250			_aSecond Edition.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_aXVI, 486 p. 18 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v135
505	0		_aPreliminaries -- Preliminaries -- Basic Linear Algebra -- Vector 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 -- Topics -- 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.
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 many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance.
650		0	_aMathematics.
650		0	_aMatrix theory.
650		0	_aAlgebra.
650	1	4	_aMathematics.
650	2	4	_aLinear and Multilinear Algebras, Matrix Theory.
655		7	_aElectronic books. _2local
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387247663
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v135
856	4	0	_uhttp://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/0-387-27474-X
912			_aZDB-2-SMA
942			_2lcc _cEBOOKS
999			_c243349 _d243349