Abstract
An n × 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 Nmatrix 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 their associated graphs the cycles play an important role. © 2003 Elsevier Inc. All rights reserved.
Keywords
Partial matrix Completion problem N-matrix Directed graphs
Referencia
C.M. Araújo, J.R. Torregrosa, A.M. Urbano (2003): The N-matrix completion problem under digraphs assumptions. Linear Algebra and its Applications 380 (2004) 213–225.
