000 03760nam a22004575i 4500
001 978-0-387-27474-4
003 DE-He213
005 20161121230925.0
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
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.
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://dx.doi.org/10.1007/0-387-27474-X
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c505983
_d505983