Quadratic Form

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.

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