  In this paper we study sequences of matrix polynomials that satisfy a
non-symmetric recurrence relation. To study this kind of sequences we use a
vector interpretation of the matrix orthogonality. In the context of these
sequences of matrix polynomials we introduce the concept of the generalized
matrix Nevai class and we give the ratio asymptotics between two consecutive
polynomials belonging to this class. We study the generalized matrix Chebyshev
polynomials and we deduce its explicit expression as well as we show some
illustrative examples. The concept of a Dirac delta functional is introduced.
We show how the vector model that includes a Dirac delta functional is a
representation of a discrete Sobolev inner product. It also allows to
reinterpret such perturbations in the usual matrix Nevai class. Finally, the
relative asymptotics between a polynomial in the generalized matrix Nevai class
and a polynomial that is orthogonal to a modification of the corresponding
matrix measure by the addition of a Dirac delta functional is deduced.
