Beginning with definitions and examples of inner product spaces, the text covers the direct summand theorem, diagonalization, the inertia theorem, the discrimin... » 

Beginning with definitions and examples of inner product spaces, the text covers the direct summand theorem, diagonalization, the inertia theorem, the discriminant, finite fields, hyperbolic planes, and Hermitian forms. Discussions of orthogonal similarity include the real self-adjoint case, unitary spaces, positivity and polar decomposition, and Specht's theorem. The final section on geometry examines affine planes, inner product planes, projective transformations, duality, cross ratio and harmonic range, conics, higher dimensional spaces, noncommutativity, and synthetic foundations of geometry. «