Orthogonal matrix polynomials whose differences are also orthogonal

We characterize orthogonal matrix polynomials (Pn)n whose differences (∇ Pn+1)n are also orthogonal by means of a discrete Pearson equation for the weight matrix W with respect to which the polynomials (Pn)n are orthogonal. We also construct some illustrative examples. In particular, we show that contrary to what happens in the scalar case, in the matrix orthogonality the discrete Pearson equation for the weight matrix W is, in general, independent of whether the orthogonal polynomials with respect to W are eigenfunctions of a second order difference operator with polynomial coefficients. c ⃝ 2013 Elsevier Inc. All rights reserved.