  We study the eigenvalues of non-normal square matrices of the form
A_n=U_nT_nV_n with U_n,V_n independent Haar distributed on the unitary group
and T_n real diagonal. We show that when the empirical measure of the
eigenvalues of T_n converges, and T_n satisfies some technical conditions, all
these eigenvalues lie in a single ring.
