Ray nonsingularity of cycle tree matrices

Ray nonsingular (RNS) matrices are a generalization of sign nonsingular (SNS) matrices from the real field to the complex field. A matrix with positive diagonals is called a cycle tree matrix if the adjacency structure of all the cycles in its associated digraph is a tree. In this paper, the ray nonsingularity of cycle tree matrices is studied, and a general method is given to recognize ray nonsingular cycle tree matrices.