Key points are not available for this paper at this time.
A well-known result for a singular irreducible M-matrix A is that the only nonnegative vector that belongs to the range space of A is the zero vector. In this paper, we prove an analogue of this result for the Lyapunov and Stein transformations, which act on the inner product space of real symmetric matrices.
Encinas et al. (Tue,) studied this question.