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TitleN_0 completions on partial matrices
Author(s)Araújo, C. Mendes
Torregrosa, Juan R.
Jordán, Cristina
KeywordsPartial matrix
Chordal graphs
Chordal graph
N -matrix 0
Issue date15-May-2009
JournalApplied Mathematics and Computation
Citation"Applied Mathematics and Computation". ISSN 0096-3003. 211:2 (May 2009) 303-312.
Abstract(s)An $n\times n$ matrix is called an $N_0$-matrix if all its principal minors are nonpositive. In this paper, we are interested in $N_0$-matrix completion problems, that is, when a partial $N_0$-matrix has an $N_0$-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial $N_0$-matrix does not have an $N_0$-matrix completion. Here, we prove that a combinatorially symmetric partial $N_0$-matrix, with no null main diagonal entries, has an $N_0$-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries.
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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