Ray solvable linear systems and ray S2NS matrices

Abstract

Ray solvable linear systems and ray S 2 NS matrices are complex generalizations of the sign solvable linear systems and S 2 NS matrices. We use the determinantal ray unique matrices (instead of ray nonsingular matrices) as a generalization of SNS matrices, to generalize some fundamental results of S 2 NS matrices from the real case to complex case, such as the graph theoretical characterization, the inverse ray patterns and the upper bound of the number of nonzero entries of S 2 NS matrices. The well known characterization of the sign solvable linear systems (in terms of the L-matrices and S ∗ matrices) is also generalized to ray solvable linear systems, and the relationships between the ray S ∗-matrices and real S ∗-matrices are investigated. Some examples are also given to illustrate that some results, such as the characterization of the sign inconsistent linear systems, do not carry over to the complex case.