For a vector v and an orthonormal set v₁,…,v_k, in an inner product space V, the inequality $\Vert v{\Vert }^2\ge {\sum }_1^k{|〈v,v_i〉|}^2.$ Equality holds for all v, if and only if v₁,…,v_k, is an orthonormal basis. Compare Parseval’s identity.