Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of Ln(Ω)Ln(Ω)-1 and Φn(z;Ω)Φn(z;Ω)-1 where Ω(z) = Ω(z) + zδ(z - w); |w| ＞ 1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, Ln ( @ ) means the leading coefficient of the orthonormal matrix polynomials Φn(z; @ ).Finally, we deduce the asymptotic behavior of Φn (w;Ω)Φn (w;Ω) * in the case when M=I.