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.
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