Publicação
The symmetric N-matrix completion problem
| 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. |
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| 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 |
| 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. |
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