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# Geometric Algebra

Emil Artin

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).

Bibliography.

Index.