Characterization of ray pattern matrix whose determinantal region has two components after deleting the origin |
| |
Authors: | Yue Liu Jia-Yu Shao |
| |
Institution: | a College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China b Department of Mathematics, Tongji University, Shanghai 200092, China c Department of Mathematics and Information, Yantai University, Yantai 264005, China |
| |
Abstract: | Ray nonsingular matrices are generalizations of sign nonsingular matrices. The problem of characterizing ray nonsingular matrices is still open. The study of the determinantal regions RA of ray pattern matrices is closely related to the study of ray nonsingular matrices. It was proved that if RA?{0} is disconnected, then it is a union of two opposite open sectors (or open rays). In this paper, we characterize those ray patterns whose determinantal regions become disconnected after deleting the origin. The characterization is based on three classes (F1), (F2) and (F3) of matrices, which can further be characterized in terms of the sets of the distinct signed transversal products of their ray patterns. Moreover, we show that in the fully indecomposable case, a matrix A is in the class (F1) (or (F2), respectively) if and only if A is ray permutation equivalent to a real SNS (or non-SNS, respectively) matrix. |
| |
Keywords: | 15A09 15A48 |
本文献已被 ScienceDirect 等数据库收录! |
|