  This paper is concerned with continuous dependence of the n-th eigenvalue on
self-adjoint discrete Sturm-Liouville problems. The n-th eigenvalue is
considered as a function in the space of the problems. A necessary and
sufficient condition for all the eigenvalue functions to be continuous and
several properties of the eigenvalue functions in a set of the space of the
problems are given. They play an important role in the study of continuous
dependence of the n-th eigenvalue function on the problems. Continuous
dependence of the n-th eigenvalue function on the equations and on the boundary
conditions is studied separately. Consequently, the continuity and
discontinuity of the n-th eigenvalue function are completely characterized in
the whole space of the problems. Especially, asymptotic behaviors of the n-th
eigenvalue function near each discontinuity point are given.
