03895nam 2200685Ia 450 991056130110332120170821192209.01-283-33250-797866133325091-118-16451-21-118-16454-7(CKB)2550000000054299(EBL)818912(OCoLC)772844590(SSID)ssj0000613303(PQKBManifestationID)12214607(PQKBTitleCode)TC0000613303(PQKBWorkID)10586767(PQKB)11471811(SSID)ssj0000635779(PQKBManifestationID)11392704(PQKBTitleCode)TC0000635779(PQKBWorkID)10653548(PQKB)11768060(MiAaPQ)EBC818912(PPN)197872417(EXLCZ)99255000000005429919890314e19881957 uy 0engur|n|---|||||txtccrGeometric algebra[electronic resource] /E. ArtinWiley classics library ed.New York Interscience Publishers1988, c19571 online resource (226 p.)Wiley classics libraryDescription based upon print version of record.0-471-60839-4 0-470-03432-7 Includes bibliographical references and index.Geometric Algebra; Preface; Suggestions for the Use of This Book; CONTENTS; CHAPTER I Preliminary Notions; 1. Notions of set theory; 2. Theorems on vector spaces; 3. More detailed structure of homomorphisms; 4. Duality and pairing; 5. Linear equations; 6. Suggestions for an exercise; 7. Notions of group theory; 8. Notions of field theory; 9. Ordered fields; 10. Valuations; CHAPTER II Affine and Projective Geometry; 1. Introduction and the first three axioms; 2. Dilatations and translations; 3. Construction of the field; 4. Introduction of coordinates; 5. Affine geometry based on a given field6. Desargues' theorem7. Pappus' theorem and the commutative law; 8. Ordered geometry; 9. Harmonic points; 10. The fundamental theorem of projective geometry; 11. The projective plane; CHAPTER III Symplectic and Orthogonal Geometry; 1. Metric structures on vector spaces; 2. Definitions of symplectic and orthogonal geometry; 3. Common features of orthogonal and symplectic geometry; 4. Special features of orthogonal geometry; 5. Special features of symplectic geometry; 6. Geometry over finite fields; 7. Geometry over ordered fields-Sylvester's theorem; CHAPTER IV The General Linear Group1. Non-commutative determinants2. The structure of GLn(κ); 3. Vector spaces over finite fields; CHAPTER V The Structure of Symplectic and Orthogonal Groups; 1. Structure of the symplectic group; 2. The orthogonal group of euclidean space; 3. Elliptic spaces; 4. The Clifford algebra; 5. The spinorial norm; 6. The cases dim V < 4; 7. The structure of the group Ω(V); Bibliography; IndexThis classic text, written by one of the foremost mathematicians of the 20th century, is now available in a low-priced paperback edition. Exposition is centered on the foundations of affine geometry, the geometry of quadratic forms, and the structure of the general linear group. Context is broadened by the inclusion of projective and symplectic geometry and the structure of symplectic and orthogonal groups.Wiley classics library.Algebras, LinearGeometry, ProjectiveAlgebras, Linear.Geometry, Projective.512.5Artin Emil1898-1962.82MiAaPQMiAaPQMiAaPQBOOK9910561301103321Geometric algebra96752UNINA