A note on "5 x 5 Completely positive matrices"

Hongbo Dong; Kurt Anstreicher

doi:10.1016/j.laa.2010.04.031

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A note on "5 x 5 Completely positive matrices"

Journal article

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A note on "5 x 5 Completely positive matrices"

Hongbo Dong and Kurt Anstreicher

Linear algebra and its applications, Vol.433(5), pp.1001-1004

10/15/2010

DOI: 10.1016/j.laa.2010.04.031

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Abstract

In their paper "5 x 5 Completely positive matrices", Berman and Xu (2004) [3] attempt to characterize which 5 x 5 doubly nonnegative matrices are also completely positive. Most of the analysis in [3] concerns a doubly nonnegative matrix A that has at least one off-diagonal zero component. To handle the case where A is componentwise strictly positive, Berman and Xu utilize an "edge-deletion" transformation of A that results in a matrix (A) over tilde having an off-diagonal zero. Berman and Xu claim that A is completely positive if and only if there is such an edge-deleted matrix (A) over tilde that is also completely positive. We show that this claim is false. We also show that two conjectures made in [3] regarding 5 x 5 completely positive matrices are both false. (C) 2010 Elsevier Inc. All rights reserved.

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Details

Title: Subtitle: A note on "5 x 5 Completely positive matrices"
Creators: Hongbo Dong - University of Iowa
Kurt Anstreicher - University of Iowa
Resource Type: Journal article
Publication Details: Linear algebra and its applications, Vol.433(5), pp.1001-1004
DOI: 10.1016/j.laa.2010.04.031
ISSN: 0024-3795
eISSN: 1873-1856
Publisher: Elsevier
Number of pages: 4
Language: English
Date published: 10/15/2010
Academic Unit: Industrial and Systems Engineering; Computer Science; Business Analytics
Record Identifier: 9984380543902771

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