  Starting from degree N solutions of a time dependent Schroedinger-like
equation for classical orthogonal polynomials, a linear matrix equation
describing perturbations around the N zeros of the polynomial is derived. The
matrix has remarkable Diophantine properties. Its eigenvalues are independent
of the zeros. The corresponding eigenvectors provide the representations of the
lower degree (0,1,...,N-1) polynomials in terms of the zeros of the degree N
polynomial. The results are valid universally for all the classical orthogonal
polynomials, including the Askey scheme of hypergeometric orthogonal
polynomials and its q-analogues.
