unitoid matrix is a square complex matrix that can be brought to diagonal form by a Hermitian congruence transformation. The canonical angles of a nonsingular unitoid matrix A are (up to the factor 1/2) the arguments of the eigenvalues of the cosquare of A, which is the matrix A−∗A. We derive an estimate for the derivative of an eigenvalue of the cosquare in the direction of the perturbation in A−∗A caused by a perturbation in A.
