Abstract
An n × 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. © 2005 Elsevier Inc. All rights reserved.
Keywords
Partial matrix Completion problem N-matrix Undirected graph
Referencia
C.M. Araújo, J.R. Torregrosa, A.M. Urbano (2005): The symmetric N-matrix completion problem. Linear Algebra and its Applications 406 (2005) 235–252.
