LEADER 04125nam 22007455 450 001 9910438160103321 005 20200704030301.0 010 $a3-642-30994-1 024 7 $a10.1007/978-3-642-30994-6 035 $a(CKB)3390000000030195 035 $a(EBL)994105 035 $a(OCoLC)818725987 035 $a(SSID)ssj0000746026 035 $a(PQKBManifestationID)11378864 035 $a(PQKBTitleCode)TC0000746026 035 $a(PQKBWorkID)10859929 035 $a(PQKB)11774732 035 $a(DE-He213)978-3-642-30994-6 035 $a(MiAaPQ)EBC994105 035 $a(MiAaPQ)EBC6314495 035 $a(PPN)168318199 035 $a(EXLCZ)993390000000030195 100 $a20120823d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLinear Algebra and Geometry$b[electronic resource] /$fby Igor R. Shafarevich, Alexey O. Remizov 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (535 p.) 300 $aThe original Russian edition was published as "Linejnaya algebra i geometriya" by Fizmatlit, Moscow, 2009. 311 $a3-642-30993-3 320 $aIncludes bibliographical references and index. 327 $aPreface -- Preliminaries -- 1. Linear Equations -- 2. Matrices and Determinants -- 3. Vector Spaces -- 4. Linear Transformations of a Vector Space to Itself -- 5. Jordan Normal Form -- 6. Quadratic and Bilinear Forms -- 7. Euclidean Spaces -- 8. Affine Spaces -- 9. Projective Spaces -- 10. The Exterior Product and Exterior Algebras -- 11. Quadrics -- 12. Hyperbolic Geometry -- 13. Groups, Rings, and Modules -- 14. Elements of Representation Theory -- Historical Note -- References -- Index. 330 $aThis book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements of matrix theory and continues with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but are usually not covered in such courses: exterior algebras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitely generated periodic modules (similar to Jordan normal forms of linear operators). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equations and differential geometry, as well as from mechanics and physics. 606 $aMatrix theory 606 $aAlgebra 606 $aGeometry 606 $aAssociative rings 606 $aRings (Algebra) 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aGeometry. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 14$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aAlgebra. 615 24$aGeometry. 615 24$aAssociative Rings and Algebras. 676 $a512.5 700 $aShafarevich$b Igor R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0730610 702 $aRemizov$b Alexey O$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438160103321 996 $aLinear Algebra and Geometry$92514817 997 $aUNINA