LEADER 04401nam 22005895 450 001 9910789344503321 005 20210915190255.0 010 $a1-4612-0901-3 024 7 $a10.1007/978-1-4612-0901-0 035 $a(CKB)3400000000089313 035 $a(SSID)ssj0001297406 035 $a(PQKBManifestationID)11739645 035 $a(PQKBTitleCode)TC0001297406 035 $a(PQKBWorkID)11362436 035 $a(PQKB)11175862 035 $a(DE-He213)978-1-4612-0901-0 035 $a(MiAaPQ)EBC3074003 035 $a(PPN)238032906 035 $a(EXLCZ)993400000000089313 100 $a20121227d1993 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Algebra$b[electronic resource] $eAn Introduction to Abstract Mathematics /$fby Robert J. Valenza 205 $a1st ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (XVIII, 237 p.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-94099-5 311 $a1-4612-6940-7 320 $aIncludes bibliographical references and index. 327 $a1 Sets and Functions -- 1.1 Notation and Terminology -- 1.2 Composition of Functions -- 1.3 Inverse Functions -- 1.4 Digression on Cardinality -- 1.5 Permutations -- Exercises -- 2 Groups and Group Homomorphisms -- 2.1 Groups and Subgroups -- 2.2 Group Homomorphisms -- 2.3 Rings and Fields -- Exercises -- 3 Vector Spaces and Linear Transformations -- 3.1 Vector Spaces and Subspaces -- 3.2 Linear Transformations -- 3.3 Direct Products and Internal Direct Sums -- Exercises -- 4 Dimension -- 4.1 Bases and Dimension -- 4.2 Vector Spaces Are Free -- 4.3 Rank and Nullity -- Exercises -- 5 Matrices -- 5.1 Notation and Terminology -- 5.2 Introduction to Linear Systems -- 5.3 Solution Techniques -- 5.4 Multiple Systems and Matrix Inversion -- Exercises -- 6 Representation of Linear Transformations -- 6.1 The Space of Linear Transformations -- 6.2 The Representation of Hom(kn,km) -- 6.3 The Representation of Hom(V,V?) -- 6.4 The Dual Space -- 6.5 Change of Basis -- Exercises -- 7 Inner Product Spaces -- 7.1 Real Inner Product Spaces -- 7.2 Orthogonal Bases and Orthogonal Projection -- 7.3 Complex Inner Product Spaces -- Exercises -- 8 Determinants -- 8.1 Existence and Basic Properties -- 8.2 A Nonrecursive Formula; Uniqueness -- 8.3 The Determinant of a Product; Invertibility -- Exercises -- 9 Eigenvalues and Eigenvectors -- 9.1 Definitions and Elementary Properties -- 9.2 Hermitian and Unitary Transformations -- 9.3 Spectral Decomposition -- Exercises -- 10 Triangulation and Decomposition of Endomorphisms -- 10.1 The Cayley-Hamilton Theorem -- 10.2 Triangulation of Endomorphisms -- 10.3 Decomposition by Characteristic Subspaces -- 10.4 Nilpotent Mappings and the Jordan Normal Form -- Exercises -- Supplementary Topics -- 1 Differentiation -- 2 The Determinant Revisited -- 3 Quadratic Forms -- 4 An Introduction to Categories and Functors. 330 $aBased on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aAlgebra 606 $aMatrix theory 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 615 0$aAlgebra. 615 0$aMatrix theory. 615 14$aAlgebra. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 676 $a512 686 $a15-01$2msc 700 $aValenza$b Robert J$4aut$4http://id.loc.gov/vocabulary/relators/aut$054714 906 $aBOOK 912 $a9910789344503321 996 $aLinear algebra$983097 997 $aUNINA