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TitleThe symmetric N-matrix completion problem
Author(s)Araújo, C. Mendes
Torregrosa, Juan R.
Urbano, Ana M.
KeywordsPartial matrix
Matrix completion problems
Undirected graphs
completion problem
undirected graph
Issue date1-Sep-2005
JournalLinear Algebra and its Applications
CitationAraújo, C. M., Torregrosa, J. R., & Urbano, A. M. (2005, September). The symmetric N-matrix completion problem. Linear Algebra and its Applications. Elsevier BV.
Abstract(s)An $n\times n$ 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.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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