  In this paper we characterize the definiteness of the discrete symplectic
system, study a nonhomogeneous discrete symplectic system, and introduce the
minimal and maximal linear relations associated with these systems. Fundamental
properties of the corresponding deficiency indices, including a relationship
between the number of square summable solutions and the dimension of the defect
subspace, are also derived. Moreover, a sufficient condition for the existence
of a densely defined operator associated with the symplectic system is
provided.
