On sign inconsistent linear systems Original Research Article

A linear system of equations Ax=b is called sign inconsistent if for each matrix (A′,b′) with the same sign pattern as (A,b), the corresponding linear system A′x=b′ is not solvable. Sign inconsistent linear systems have close relationships with sign solvable and conditionally sign solvable linear systems. In this paper we study various properties of sign inconsistent linear systems. We give a complete characterization of sign inconsistent linear systems in terms of L-matrices. We also obtain complete characterizations of the minimally sign inconsistent linear systems in terms of the L-canonical forms and their corresponding canonical digraphs of the barely L-matrices.