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024 7 $a10.1007/978-1-4419-8764-8
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100   $a20121227d1990      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aAbstract Linear Algebra$b[electronic resource] /$fby Morton L. Curtis
205   $a1st ed. 1990.
210  1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1990.
215   $a1 online resource (X, 168 p. 1 illus.) 
225 1 $aUniversitext,$x0172-5939
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-387-97263-3 
320   $aIncludes bibliographical references and index.
327   $a0. Algebraic Preliminaries -- I. Vector Spaces and Linear Maps -- A. Vector Spaces -- B. Linear Maps -- C. Bases, Dimension -- D. Direct Sums, Quotients -- E. Eigenvectors and Eigenvalues (Part i) -- F. Dual Spaces -- II. Matrices and Determinants -- A. Matrices -- B. Algebras -- C. Determinants, the Laplace Expansion -- D. Inverses, Systems of Equations -- E. Eigenvalues (Part ii) -- III. Rings and Polynomials -- A. Rings -- B. Polynomials -- C. Cayley-Hamilton Theorem -- D. Spectral Theorems -- E. Jordan Form -- IV. Inner Product Spaces -- A. Rn as a Model, Bilinear Forms -- B. Real Inner Product Spaces, Normed Vector Spaces -- C. Complex Inner Product Spaces -- D. Orthogonal and Unitary Groups -- E. Stable Subspaces for Unitary and Orthogonal Groups -- V. Normed Algebras -- A. The Normed Algebras R and C -- B. Some General Results, Quaternions -- C. Alternative and Division Algebras -- D. Cayley-Dickson Process, Hurwitz Theorem.
330   $aBeginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. Unique in presenting this material at an elementary level, the book stresses the complete logical development of the subject and will provide a bavuable reference for mathematicians in general.
410  0$aUniversitext,$x0172-5939
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   $aCurtis$b Morton L$4aut$4http://id.loc.gov/vocabulary/relators/aut$045893
906   $aBOOK
912   $a9910480731603321
996   $aAbstract linear algebra$9382827
997   $aUNINA