  In this paper, inequalities among eigenvalues of different self-adjoint
discrete Sturm-Liouville problems are established. For a fixed discrete
Sturm-Liouville equation, inequalities among eigenvalues for different boundary
conditions are given. For a fixed boundary condition, inequalities among
eigenvalues for different equations are given. These results are obtained by
applying continuity and discontinuity of the n-th eigenvalue function,
monotonicity in some direction of the n-th eigenvalue function, which were
given in our previous papers, and natural loops in the space of boundary
conditions. Some results generalize the relevant existing results about
inequalities among eigenvalues of different Sturm-Liouville problems.
