Journal or Book Title
Electronic Journal of Linear Algebra
A real n x n matrix is a Q-matrix if for every k = 1, 2, . . . , n the sum of all k x k principal minors is positive. A digraph D is said to have Q-completion if every partial Q-matrix specifying D can be completed to a Q-matrix. For the Q-completion problem, sufficient conditions for a digraph to have Q-completion are given, necessary conditions for a digraph to have Q-completion are provided, and those digraphs of order at most four that have Q-completion are characterized.
DeAlba, Luz Maria; Hogben, Leslie; and Sarma, Bhaba Kumar, "The Q-matrix completion problem" (2009). Mathematics Publications. 243.