N-matrix completion problem

• Author(s): Araújo, C. Mendes ; Torregrosa, Juan R. ; Urbano, Ana M.
• Date: 2003
• Persistent ID: http://hdl.handle.net/1822/1471
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Partial Matrix; Matrix completion problem; N-matrix; Undirected graphs
• Document Type: Article
• Language: English

Description

An n x n matrix is called an N-matrix if all principal minors are negative. In this paper, we are interested in N-matrix completion problems, that is, when a partial N-matrix hás an N-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N-matrix does not have an N-matrix completion. Here we prove that a combinatorially symmetric partial N-matrix has an N-matrix completion if the graph of its specified entries is a 1-chordal graph. We also prove that there exists an N-matrix completion for a partial N-matrix whose associated graph is an undirected cycle.