John Wiley & Sons, 9 sept. 2011 - 224 pages
This 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.
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additive assume axiom basis becomes called canonical Chapter characteristic commutative condition consequently consider consists construct contains correspondence coset deﬁned deﬁnition denote Desargues described determinant dilatation dimension direction distinct element equations equivalent exists factor ﬁeld ﬁnd ﬁnite ﬁrst ﬁxed function geometry given gives hence holds homomorphism hyperbolic hyperplane identity implies independent induces invariant inverse isometry isomorphism isotropic vectors keeps kernel leaves lies linear matrix means move multiplication non-singular non-zero obtain obviously one-to-one orthogonal pairing parallel plane positive possible projective Proof prove range reader replace respect rotation rule satisﬁes shows side simple space square subgroup subspace Suppose symmetries symplectic theorem trace translation transvection true unique unit vector vector space write