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The symmetric N-matrix completion problem

✍ Scribed by C. Mendes Araújo; Juan R. Torregrosa; Ana M. Urbano

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 261 KB
Volume: 406
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.04.008

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✦ Synopsis

An n × n matrix is called an N -matrix if all its principal minors are negative. In this paper, we are interested in the symmetric N -matrix completion problem, that is, when a partial symmetric N -matrix has a symmetric N -matrix completion. Here, we prove that a partial symmetric N -matrix has a symmetric N -matrix completion if the graph of its specified entries is chordal. Furthermore, if this graph is not chordal, then examples exist without symmetric N -matrix completions. Necessary and sufficient conditions for the existence of a symmetric N -matrix completion of a partial symmetric N -matrix whose associated graph is a cycle are given.

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