The P_0^+-matrix completion problem

Abstract

A real n by n matrix B is a P_0^+ -matrix if for each k in {1, 2, . . . , n} every k by k principal minor of B is nonnegative, and at least one k by k principal minor is positive. A digraph D is said to have P_0^+-completion if every partial P_0^+-matrix specifying D can be completed to a P_0^+ -matrix. In this paper, we study the P_0^+-completion problem, give necessary conditions for a digraph to have P_0^+-completion, and single out those digraphs of order at most four that have P_0^+-completion.