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

Immanuel M. Bomze; Werner Schachinger; Reinhard Ullrich

doi:10.1016/j.laa.2014.06.025

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

Immanuel M. Bomze, Werner Schachinger, Reinhard Ullrich

Department of Statistics and Operations Research

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study n×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.

Original language	English
Pages (from-to)	208-221
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	459
DOIs	https://doi.org/10.1016/j.laa.2014.06.025
Publication status	Published - 15 Oct 2014

Austrian Fields of Science 2012

101015 Operations research

Keywords

Copositive optimization
Completely positive matrices
Cp-rank
Nonnegative factorization
Circular symmetry
COPOSITIVE OPTIMIZATION

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10.1016/j.laa.2014.06.025

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abstract = "We study n×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.",

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AB - We study n×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.

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KW - Completely positive matrices

KW - Cp-rank

KW - Nonnegative factorization

KW - Circular symmetry

KW - COPOSITIVE OPTIMIZATION

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JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

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

Abstract

Austrian Fields of Science 2012

Keywords

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