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In the setting of real square matrices, it is known that, if $A$ is asingular irreducible $M$-matrix, then the only nonnegative vector that belongsto the range space of $A$ is the zero vector. In this paper, we prove ananalogue of this result for the Lyapunov and the Stein operators.

On an Analogue of a Property of Singular $M$-matrices, for the Lyapunov and the Stein Operators