Extended M-matrices and subtangentiality

The concept of a singular M-matrix A with respect to a proper cone X is extended, by replacing the usual regularity condition A = al - B for a Xnonnegative matrix B with the weaker condition, exponential nonnegativity of - A. As in earlier work which dealt with the nonsingular case, in the present characterizations the lack of regularity is overcome by employing subtangentiality.