-
Let
be a vector space over . A function is called a quadratic form if there exists a symmetric bilinear form such that -
(Friedberg e6.7.15) If
is a field not of characteristic two, then -
(Friedberg 6.30.1) Let
be a quadratic form on a finite dimensional real inner product space. There exists an orthonormal basis for and scalars such that if and for
. Then If
is the symmetric bilinear form associated by , then can be chosen to be any orthonormal basis for for which is a diagonal matrix. -
A subspace
is totally isotropic if