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.
· Partial table of contents:
· Theorems on Vector Spaces.
· More Detailed Structure of Homomorphisms.
· Duality and Pairing.
Affine and Projective Geometry.
· Dilations and Translations.
· Construction of the Field.
· The Fundamental Theorem of Projective Geometry.
· The Projective Plane.
Symplectic and Orthogonal Geometry.
· Metric Structures on Vector Spaces.
· Common Features of Orthogonal and Symplectic Geometry.
· 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.
· The Orthogonal Group of Euclidean Space.
· Elliptic Spaces.
· The Spinorial Norm.
· The Structure of the Group omega(X).