In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals $F$ associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of $F$ with separated endpoints, (ii) a characterization of the nonnegativity of $F$ for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of $F$ with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.

Last change: September 29, 2005. (c) Roman Hilscher