LEADER 04009nam 22006255 450 001 996466610403316 005 20230217110930.0 010 $a3-540-46867-6 024 7 $a10.1007/BFb0083581 035 $a(CKB)1000000000437401 035 $a(SSID)ssj0000325416 035 $a(PQKBManifestationID)12049792 035 $a(PQKBTitleCode)TC0000325416 035 $a(PQKBWorkID)10321715 035 $a(PQKB)10827809 035 $a(DE-He213)978-3-540-46867-7 035 $a(MiAaPQ)EBC5579578 035 $a(Au-PeEL)EBL5579578 035 $a(OCoLC)1066176829 035 $a(MiAaPQ)EBC6842166 035 $a(Au-PeEL)EBL6842166 035 $a(OCoLC)1120881620 035 $a(DE-He213)978-0-387-72831-5 035 $a(PPN)155168193 035 $a(EXLCZ)991000000000437401 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAdvanced Linear Algebra$b[electronic resource] /$fby Steven Roman 205 $a3rd ed. 2008. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2008. 215 $a1 online resource (VIII, 228 p.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v135 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-51970-X 311 $a3-540-51970-X 327 $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. 330 $aFor the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v135 606 $aAlgebras, Linear 606 $aLinear Algebra 615 0$aAlgebras, Linear. 615 14$aLinear Algebra. 676 $a519.3 700 $aDolecki$b Szymon$0535043 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466610403316 996 $aAdvanced Linear Algebra$93091286 997 $aUNISA