000 03643nam a22004575i 4500
001 978-0-387-72831-5
003 DE-He213
005 20161121231207.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387728315
_9978-0-387-72831-5
024 7 _a10.1007/978-0-387-72831-5
_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 _aThird Edition.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aXVIII, 526 p.
_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 _aBasic 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 -- Singular Values and the Moore–Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus.
520 _aFor the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online.
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:
_z9780387728285
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v135
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-72831-5
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509931
_d509931