A note on "5 x 5 Completely positive matrices"

作者：Dong Hongbo; Anstreicher Kurt^*

来源：Linear Algebra and Its Applications, 2010, 433(5): 1001-1004.

DOI：10.1016/j.laa.2010.04.031

• Completely positive matrices
• Doubly nonnegative matrices
• Copositive matrices

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.

• 出版日期2010-10-15