LEADER 03810nam 22006255 450 001 9910300259803321 005 20200704001212.0 010 $a3-319-24346-2 024 7 $a10.1007/978-3-319-24346-7 035 $a(CKB)3710000000521713 035 $a(SSID)ssj0001585268 035 $a(PQKBManifestationID)16265209 035 $a(PQKBTitleCode)TC0001585268 035 $a(PQKBWorkID)14864820 035 $a(PQKB)10215364 035 $a(DE-He213)978-3-319-24346-7 035 $a(MiAaPQ)EBC6315257 035 $a(MiAaPQ)EBC5592134 035 $a(Au-PeEL)EBL5592134 035 $a(OCoLC)932169329 035 $a(MnU)OTLid0000188 035 $a(PPN)190532289 035 $a(EXLCZ)993710000000521713 100 $a20151120d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Algebra$b[electronic resource] /$fby Jörg Liesen, Volker Mehrmann 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XI, 324 p. 22 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-24344-6 327 $aLinear Algebra in every day life -- Basic mathematical concepts -- Algebraic structures -- Matrices -- The echelon form and the rank of matrices -- Linear systems of equations -- Determinants of matrices -- The characteristic polynomial and eigenvalues of matrices -- Vector spaces -- Linear maps -- Linear forms and bilinear forms -- Euclidean and unitary vector spaces -- Adjoints of linear maps -- Eigenvalues of endomorphisms -- Polynomials and the Fundamental Theorem of Algebra -- Cyclic subspaces, duality and the Jordan canonical form -- Matrix functions and systems of differential equations -- Special classes of endomorphisms -- The singular value decomposition -- The Kronecker product and linear matrix equations. 330 $aThis self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ?MATLAB-Minutes? students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aMatrix theory 606 $aAlgebra 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aMatrix theory. 615 0$aAlgebra. 615 14$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512.5 700 $aLiesen$b Jörg$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755674 702 $aMehrmann$b Volker$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300259803321 996 $aLinear Algebra$92527088 997 $aUNINA