Weak duality theorem and complementary slackness theorem for linear matrix programming problems

In this paper we present a weak duality theorem and a complementary slackness theorem, which were omitted from the duality theory of the Gale-Kuhn-Tucker matrix optimization problem. We also show that the results are closely related to the duality of multiple-criteria and multiple-constraint level (MC^2) programming and the duality of multiobjective linear programming respectively.