A note on “ 5 × 5 Completely positive matrices ”
نویسنده
چکیده
In their paper “5×5 Completely positive matrices,” Berman and Xu [BX04] attempt to characterize which 5× 5 doubly nonnegative matrices are also completely positive. Most of the analysis in [BX04] 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 à 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 à that is also completely positive. We show that this claim is false. We also show that two conjectures made in [BX04] regarding 5× 5 completely positive matrices are both false.
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