From seven to eleven: Completely positive matrices with high cp-rank

We study n x n completely positive matrices M on the boundary of the completely positive cone, namely those orthogonal to a copositive matrix S which generates a quadratic form with finitely many zeroes in the standard simplex. Constructing particular instances of S, we are able to construct counterexamples to the famous Drew Johnson Loewy conjecture (1994) for matrices of order seven through eleven. (C) 2014 Elsevier Inc. All rights reserved.