Nonnegative P 0 -matrix completion problem

Abstract

A partial matrix is a matrix with some entries specified while the other unspecified entries are free to be chosen. Completion of partial matrix is a specific choice of unspecified entries such that the resulting matrix satisfies a certain property. This study considers nonnegative P 0 -matrix completion. The nonnegative P - matrix completion problem determines patterns of positions with the property that any partial nonnegative P 0 -matrix that specifies the pattern can be completed to a nonnegative P -matrix. In particular the study focusses on real 5x5 partial nonnegative P 0 0 -matrices specifying digraphs for p = 5 and q = 3, where p is the number of vertices and q is the number of arcs. The study establishes that all digraphs for p = 5, q = 3 which are either cycles or acyclic digraphs have zero completion to nonnegative P 0 -completion. 0