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Geometric algebra.

Author: Emil Artin
Publisher: New York, Interscience Publishers [1957]
Series: Interscience tracts in pure and applied mathematics, no. 3.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Artin, Emil, 1898-1962.
Geometric algebra.
New York, Interscience Publishers [1957]
(OCoLC)904150131
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Emil Artin
ISBN: 0470034327 9780470034323
OCLC Number: 529662
Description: 214 pages 24 cm.
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).
Series Title: Interscience tracts in pure and applied mathematics, no. 3.

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