Let A / V -> W be a nonsingular linear map of vector spaces V and W of dimension 2 and endowed with inner products (,) and (,), respectively. A is a similitude if there exists a real number lambda ne0 such that (A*v_1, A*v_2) = lambdalanglev_1, v_2rangle for all vectors v_1 , v_2 in V Assume that A is not a similitude and show that there exists a unique pair of orthonormal vectors e_1 and e_2 in V such that A*e_1 A*e_2 are orthogonal in W.
