Linear systems with signed solutions Original Research Article

Linear systems, Ax=b, for which the sign patterns A and b completely determine the set of sign patterns of vectors in the solution set are studied. These systems generalize the existing notion of sign-solvable linear systems. Linear systems with signed solutions are characterized in terms of two classes of matrices. The first class, L-matrices, plays a central role in the study of sign-solvable linear systems. The second class is new and generalizes the class of S*-matrices that arise in sign-solvable linear systems. Several constructions for the new class of matrices are given.