A forbidden structure of ray nonsingular matrices

• DOI: 10.1016/j.laa.2013.07.015
• Publication Date: 2013-07-27T01:01:23Z
• Authors: Yue Liu; Hai-Ying Shan
• Keywords: Digraph; Matrix (chemical analysis)

Abstract A complex square matrix is called a ray nonsingular matrix (RNS matrix) if its ray pattern implies that it is nonsingular. In this paper, a necessary condition for RNS matrices is provided by showing that if A = I − A ( D ) is ray nonsingular, then the arc weighted digraph D contains no forbidden cycle chains.