For every completely positive matrix A, cp-rankA â‰¥ rankA. Let cp-rankG be the maximal cp-rank of a CP matrix realization of G. Then for every graph G on n vertices, cp-rankG â‰¥ n. In this paper theâ€¦ (More)

We describe the main open problems which are currently of interest in the theory of copositive and completely positive matrices. We give motivation as to why these questions are relevant and provideâ€¦ (More)

We show that the maximal cp-rank of nÃ—n completely positive matrices is attained at a positive-definite matrix on the boundary of the cone of nÃ—n completely positive matrices, thus answering a longâ€¦ (More)

The cp-rank of a graph G, cpr(G), is the maximum cp-rank of a completely positive matrix with graph G. One obvious lower bound on cpr(G) is the (edge-) clique covering number, cc(G), i.e., theâ€¦ (More)

Hiriart-Urruty and Seeger have posed the problem of finding the maximal possible angle Î¸max(Cn) between two copositive matrices of order n [J.-B. Hiriart-Urruty and A. Seeger. A variational approachâ€¦ (More)

We consider two generalizations of the notion of a Soules basis matrix. A pair of nonsingular n Ã— n matrices (P, Q) is called a double Soules pair if the first columns of P and Q are positive, PQT =â€¦ (More)

A block graph is a graph in which every block is a complete graph (clique). Let G be a block graph and let A(G) be its (0,1)-adjacency matrix. Graph G is called nonsingular (singular) if A(G) isâ€¦ (More)