Let {y^k} be a set of orthonormal vectors with k = 1, 2, ..., K, such that the inner product (y^k, y^k) = 1. Then set x = sum_(k = 1)^K u_k y^k so that for any square matrix A for which the product A x is defined, the corresponding quadratic form is (x, A x) = sum_(k, l = 1)^K u_k u_l(y^k, A y^l).

Henri Poincaré