The N-matrix completion problem under digraphs assumptions Original Research Article

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 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 their associated graphs the cycles play an important role.