04125nam 22007455 450 991043816010332120200704030301.03-642-30994-110.1007/978-3-642-30994-6(CKB)3390000000030195(EBL)994105(OCoLC)818725987(SSID)ssj0000746026(PQKBManifestationID)11378864(PQKBTitleCode)TC0000746026(PQKBWorkID)10859929(PQKB)11774732(DE-He213)978-3-642-30994-6(MiAaPQ)EBC994105(MiAaPQ)EBC6314495(PPN)168318199(EXLCZ)99339000000003019520120823d2013 u| 0engur|n|---|||||txtccrLinear Algebra and Geometry[electronic resource] /by Igor R. Shafarevich, Alexey O. Remizov1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (535 p.)The original Russian edition was published as "Linejnaya algebra i geometriya" by Fizmatlit, Moscow, 2009.3-642-30993-3 Includes bibliographical references and index.Preface -- 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.This 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.Matrix theoryAlgebraGeometryAssociative ringsRings (Algebra)Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Matrix theory.Algebra.Geometry.Associative rings.Rings (Algebra).Linear and Multilinear Algebras, Matrix Theory.Algebra.Geometry.Associative Rings and Algebras.512.5Shafarevich Igor Rauthttp://id.loc.gov/vocabulary/relators/aut730610Remizov Alexey Oauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910438160103321Linear Algebra and Geometry2514817UNINA