LEADER 03868nam 2200685Ia 450 001 9910877477003321 005 20200520144314.0 010 $a1-283-33250-7 010 $a9786613332509 010 $a1-118-16451-2 010 $a1-118-16454-7 035 $a(CKB)2550000000054299 035 $a(EBL)818912 035 $a(OCoLC)772844590 035 $a(SSID)ssj0000613303 035 $a(PQKBManifestationID)12214607 035 $a(PQKBTitleCode)TC0000613303 035 $a(PQKBWorkID)10586767 035 $a(PQKB)11471811 035 $a(SSID)ssj0000635779 035 $a(PQKBManifestationID)11392704 035 $a(PQKBTitleCode)TC0000635779 035 $a(PQKBWorkID)10653548 035 $a(PQKB)11768060 035 $a(MiAaPQ)EBC818912 035 $a(PPN)197872417 035 $a(EXLCZ)992550000000054299 100 $a19890314e19881957 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric algebra /$fE. Artin 205 $aWiley classics library ed. 210 $aNew York $cInterscience Publishers$d1988, c1957 215 $a1 online resource (226 p.) 225 1 $aWiley classics library 300 $aDescription based upon print version of record. 311 $a0-471-60839-4 311 $a0-470-03432-7 320 $aIncludes bibliographical references and index. 327 $aGeometric 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 field 327 $a6. 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 Group 327 $a1. Non-commutative determinants2. The structure of GLn(?); 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 ?(V); Bibliography; Index 330 $aThis classic text, written by one of the foremost mathematicians of the 20th century, is now available in a low-priced paperback edition. Exposition is centered on the foundations of affine geometry, the geometry of quadratic forms, and the structure of the general linear group. Context is broadened by the inclusion of projective and symplectic geometry and the structure of symplectic and orthogonal groups. 410 0$aWiley classics library. 606 $aAlgebras, Linear 606 $aGeometry, Projective 615 0$aAlgebras, Linear. 615 0$aGeometry, Projective. 676 $a512.5 700 $aArtin$b Emil$f1898-1962.$082 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910877477003321 996 $aGeometric algebra$996752 997 $aUNINA