Rectangular L-matrices

AbstractAn L-matrix is an m-by-n (0, 1, -1)-matrix A such that every m-by-n real matrix with the same sign pattern as A has linearly independent rows. The most widely studied L-matrices are the square L-matrices, also called sign-nonsingular matrices. In this paper we investigate rectangular L-matrices. We obtain and study a decomposition theorem for L-matrices. We introduce two new classes of L-matrices, which for square matrices reduce to sign-nonsingular matrices. The maximum number of columns for matrices in each of these classes is obtained, and those matrices attaining the maximum are characterized