A miraculously commuting family of orthogonal matrix polynomials satisfying second order differential equations Original Research Article

We find structural formulas for a family image of matrix polynomials of arbitrary size orthogonal with respect to the weight matrix image, where image is certain nilpotent matrix. It turns out that this family is a paradigmatic example of the many new phenomena that show the big differences between scalar and matrix orthogonality. Surprisingly, the polynomials image, image, form a commuting family. This commuting property is a genuine and miraculous matrix setting because, in general, the coefficients of image do not commute with those of image, image.