Orthogonal matrix polynomials: zeros and Blumenthal's theorem
Journal of Approximation Theory
Matrix orthogonal polynomials whose derivatives are also orthogonal
Journal of Approximation Theory
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We find structural formulas for a family (P"n)"n of matrix polynomials of arbitrary size orthogonal with respect to the weight matrix e^-^t^^^2e^A^te^A^^^*^t, where A 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 P"n, n=0, form a commuting family. This commuting property is a genuine and miraculous matrix setting because, in general, the coefficients of P"n do not commute with those of P"m, nm.