The doubly negative matrix completion problem

• Autor(a) principal: Araújo, C. Mendes
• Data de Publicação: 2005
• Outros Autores: Torregrosa, Juan R., Urbano, Ana M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/1502
• topic: Partial matrix; Matrix completion problems; DN-matrix; Undirected graphs; matrix completion problem; Science & Technology

An $n\times n$ matrix over the field of real numbers is a doubly negative matrix if it is symmetric, negative definite and entry-wise negative. In this paper, we are interested in the doubly negative matrix completion problem, that is when does a partial matrix have a doubly negative matrix completion. In general, we cannot guarantee the existence of such a completion. In this paper, we prove that every partial doubly negative matrix whose associated graph is a $p$-chordal graph $G$ has a doubly negative matrix completion if and only if $p=1$. Furthermore, the question of completability of partial doubly negative matrices whose associated graphs are cycles is addressed.