- From seven to eleven: completely positive matrices with high cp-rank Immanuel Bomze (immanuel.bomzeunivie.ac.at) Werner Schachinger (werner.schachingerunivie.ac.at) Reinhard Ullrich (reinhard.ullrichunivie.ac.at) Abstract: We study $n\times n$ 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. Keywords: copositive optimization, completely positive matrices, cp-rank, nonnegative factorization, circular symmetry Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: Preprint NI14007-POP, Isaac Newton Institute for Mathematical Sciences, University of Cambridge UK, accepted for publication in: Linear Alg. Appl. Download: [PDF]Entry Submitted: 01/17/2014Entry Accepted: 01/17/2014Entry Last Modified: 06/19/2014Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.