The Q-matrix completion problem

Date
2009-03-01
Authors
DeAlba, Luz
Hogben, Leslie
Hogben, Leslie
Sarma, Bhaba
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Altmetrics
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Research Projects
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Mathematics
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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.

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<p>This article is published as DeAlba, Luz, Leslie Hogben, and Bhaba Sarma. "The Q-matrix completion problem." <em>The Electronic Journal of Linear Algebra</em> 18 (2009): 176-191. DOI: <a href="https://doi.org/10.13001/1081-3810.1303" target="_blank">10.13001/1081-3810.1303</a>. Posted with permission.</p>
Keywords
Partial matrix, Matrix completion, Q-matrix, Q-completion, Digraph
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