On a Christoffel Transformation for Matrix Measures Supported on the Unit Circle

Let σ be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of σ defined by dσcm(z)=Wm(z)Hdσ(z)Wm(z),where Wm(z)=∏j=1m(zI-Aj) and A_j is a square matrix for j= 1 , … , m. Moreover, we study the relative asymptotics of the associated orthogonal matrix polynomials when σcm satisfies a matrix condition in the diagonal case. Some illustrative examples are considered.