  The main aim of this work is to apply the study of the asymptotic behaviour
of generalized eigenvalues between infinite Hermitian definite positive
matrices in an important question regarding the location of zeros of Sobolev
orthogonal polynomials. In order to do it we introduce matrix Sobolev inner
products associated with a set of infinite Hermitian positive definite matrices
that generalize a type of Sobolev inner products. These matrix components are
not necessarily moment matrices associated to measures. This general framework
allows us to study boundedness of multiplication operator in the space of
polynomials, that is a sufficient condition for boundedness of zeros of
orthogonal polynomials, via this matrix approach. As a consequence of our
results we provide a criteria to assure boundedness of the zero set of Sobolev
orthogonal polynomials in different situations in terms of the generalized
eigenvalues introduced in [10].
