Matrix moment perturbations and the inverse Szegö matrix transformation

Given a perturbation of a matrix measure supported on the unit circle, we analyze the perturbation obtained on the corresponding matrix measure on the real line, when both measures are related through the Szegö matrix transformation. Moreover, using the connection formulas for the corresponding sequences of matrix orthogonal polynomials, we deduce several properties such as relations between the corresponding norms. We illustrate the obtained results with an example.