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

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

Access to Document

10.1016/j.laa.2014.06.025

Cite this

@article{a35b0928acfe4b3daf39c35da6b5832f,

title = "From seven to eleven: Completely positive matrices with high cp-rank",

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.",

keywords = "Copositive optimization, Completely positive matrices, Cp-rank, Nonnegative factorization, Circular symmetry, COPOSITIVE OPTIMIZATION",

author = "Bomze, \{Immanuel M.\} and Werner Schachinger and Reinhard Ullrich",

year = "2014",

month = oct,

day = "15",

doi = "10.1016/j.laa.2014.06.025",

language = "English",

volume = "459",

pages = "208--221",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

}

TY - JOUR

T1 - From seven to eleven

T2 - Completely positive matrices with high cp-rank

AU - Bomze, Immanuel M.

AU - Schachinger, Werner

AU - Ullrich, Reinhard

PY - 2014/10/15

Y1 - 2014/10/15

N2 - 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.

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.

KW - Copositive optimization

KW - Completely positive matrices

KW - Cp-rank

KW - Nonnegative factorization

KW - Circular symmetry

KW - COPOSITIVE OPTIMIZATION

UR - https://www.scopus.com/pages/publications/84905021024

U2 - 10.1016/j.laa.2014.06.025

DO - 10.1016/j.laa.2014.06.025

M3 - Article

SN - 0024-3795

VL - 459

SP - 208

EP - 221

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

Abstract

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Cite this