The N-matrix completion problem under digraphs assumptions

• Author(s): Araújo, C. Mendes ; Torregrosa, Juan R. ; Urbano, Ana M.
• Date: 2004
• Persistent ID: http://hdl.handle.net/1822/2870
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Partial matrix; Matrix completion problems; N-matrix; Digraph
• Document Type: Article
• Language: English

Description

An $n \times n$ matrix is called an $N$--matrix if all principal minors are negative. In this paper, we are interested in the partial $N$--matrix completion problem, when the partial $N$--matrix is non-combinatorially symmetric. In general, this type of partial matrices does not have an $N$--matrix completion. We prove that a non-combinatorially symmetric partial $N$--matrix has an $N$--matrix completion if the graph of its specified entries is an acyclic graph or a cycle. We also prove that there exists the desired completion for partial $N$--matrices such that in its associated graphs the cycles play an important role.