A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R which satisfies Q(v, w) = Q(w, v). For example, if A is a n×n symmetric matrix, then Q(v, w) = v^T A w = 〈v, A w〉 is a symmetric bilinear form. Consider A = [1 | 2 2 | -3], then Q((a_1, a_2), (b_1, b_2)) = a_1 b_1 + 2a_1 b_2 + 2a_2 b_1 - 3a_2 b_2.

diagonal quadratic form | field | Hilbert symbol | inner product | p-adic number | quadratic form | vector space