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Geometric algebra.


New York, Interscience Publishers [1957] .
ISBN 0471608394, 0470034327, 9780470034323

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Subjects Algebraische Geometrie.
Algebras, Linear.
Algèbre linéaire.
Geometrische Algebra.
Geometry, Projective.
Géométrie projective.
Series Interscience tracts in pure and applied mathematics ; no. 3.
Description 214 pages 24 cm.
Copyright Date [1957]
Notes Includes bibliographical references (page 212) and index.
Contents Preface -- Suggestions for the use of the book -- Preliminary notions. Notions of set theory ; Theorems on vector spaces ; More detailed structure of homomorphisms ; Duality and pairing ; Linear equations ; Suggestions for an exercise ; Notions of group theory ; Notions of field theory ; Ordered fields ; Valuations -- Affine and projective geometry. Introduction and the first three axioms ; Dilatations and translations ; Construction of the field ; Introduction of coordinates ; Affine geometry based on a given field ; Desargues' theorem ; Pappus' theorem and the commutative law ; Ordered geometry ; Harmonic points ; The fundamental theorem of projective geometry ; The projective plane -- Symplectic and orthogonal geometry. Metric structures on vector spaces ; Definitions of symplectic and orthogonal geometry ; Common features of orthogonal and symplectic geometry ; Special features of orthogonal geometry ; Special features of symplectic geometry ; Geometry over finite fields ; Geometry over ordered fields -- Sylvester's theorem -- The general linear group. Non-commutative determinants ; The structure of GLn(k) ; Vector spaces over finite fields -- The structure of symplectic and orthogonal groups. Structure of the symplectic group ; The orthogonal group of euclidean space ; Elliptic spaces ; The Clifford algebra ; The spinorial norm ; The cases dim V <̲ 4 ; The structure of the group [omega](V).
Network Numbers (OCoLC)529662
(OCoLC)ocm00529662
WorldCat Search OCLC WorldCat
WorldCat Identities Artin, Emil, 1898-1962.
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