Coherent pairs and Sobolev-type orthogonal polynomials on the real line: An extension to the matrix case

In this contribution, we extend the concept of coherent pair for two quasi-definite matrix linear functionals u₀ and u₁. Necessary and sufficient conditions for these functionals to constitute a coherent pair are determined, when one of them satisfies a matrix Pearson-type equation. Moreover, we deduce algebraic properties of the matrix orthogonal polynomials associated with the Sobolev-type inner product 〈p,q〉_s=〈p,q〉_u0+〈p^′M₁,q^′M₂〉_u1, where M₁ and M₂ are m×m non-singular matrices and p,q are matrix polynomials.