Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

3-2009

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

18

First Page

176

Last Page

191

DOI

10.13001/1081-3810.1303

Abstract

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.

Comments

This article is published as DeAlba, Luz, Leslie Hogben, and Bhaba Sarma. "The Q-matrix completion problem." The Electronic Journal of Linear Algebra 18 (2009): 176-191. DOI: 10.13001/1081-3810.1303. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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