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The symmetric N-matrix completion problem

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Resumo: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.
Autores principais:Araújo, C. Mendes
Outros Autores:Torregrosa, Juan R.; Urbano, Ana M.
Assunto:Partial matrix Matrix completion problems N-matrix Undirected graphs completion problem undirected graph
Ano:2005
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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