  In this paper we consider random block matrices, which generalize the general
beta ensembles, which were recently investigated by Dumitriu and Edelmann
(2002, 2005). We demonstrate that the eigenvalues of these random matrices can
be uniformly approximated by roots of matrix orthogonal polynomials which were
investigated independently from the random matrix literature. As a consequence
we derive the asymptotic spectral distribution of these matrices. The limit
distribution has a density, which can be represented as the trace of an
integral of densities of matrix measures corresponding to the Chebyshev matrix
polynomials of the first kind. Our results establish a new relation between the
theory of random block matrices and the field of matrix orthogonal polynomials,
which have not been explored so far in the literature.
