Home > ELA > Vol. 29 (2015)

#### Article Title

#### Keywords

Partial matrix, Matrix completion, P_0^+ -matrix, P_0^+-completion, digraph.

#### 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.

#### Recommended Citation

Sarma, Bhaba Kumar and Sinha, Kalyan.
(2015),
"The P_0^+-matrix completion problem",
*Electronic Journal of Linear Algebra*,
Volume 29, pp. 120-143.

DOI: http://dx.doi.org/10.13001/1081-3810.2997

*Abstract*