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We consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm-Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness remained an open problem. In this paper we present the solution to this problem and offer necessarydoi:10.1017/s0013091502001086 fatcat:ol7p3hwk4zbibaagqqyfuki4iu