Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices

Let $\{c_j\}_{j=0}^{n}$ be a sequence of matrix moments associated with a matrix of measures supported on the unit circle, and let $\{P_j\}_{j=0}^{n}$ be its corresponding sequence of monic matrix orthogonal polynomials. In this contribution, we consider a perturbation on the moments and find an explicit relation for the perturbed orthogonal polynomials in terms of $\{P_j\}_{j=0}^{n}$. We also obtain an expression for the corresponding second kind polynomials.