Conditional sign-solvability

Sign-solvable linear systems were introduced by economists in modelling economic systems where only qualitative information is known. We introduce the idea of a conditionally sign-solvable linear system [email protected] = b by relaxing the definition of sign-solvability so as not to require that each linear system with the same sign pattern as [email protected] = b has a solution. Conditional sign-solvability is more widely applicable than sign-solvability. We show that the study of conditional sign-solvability reduces to the study of L-matrices and matrices that we call conditionally S^*-matrices. Some basic properties of conditionally S^*-matrices are obtained.