On the classes of fully copositive and fully semimonotone matrices Original Research Article

In this paper we consider the class C0f of fully copositive and the class E0f of fully semimonotone matrices. We show that C0f matrices with positive diagonal entries are column sufficient. We settle a conjecture made by Murthy and Parthasarathy to the effect that a C0f∩Q0 matrix is positive semidefinite by providing a counterexample. We finally consider E0f matrices introduced by Cottle and Stone (Math. Program. 27 (1983) 191–213) and partially address Stoneʹs conjecture to the effect that E0f∩Q0subset of or equal toP0 by showing that E0f∩Dc matrices are P0, where Dc is the Doverspike class of matrices.