An example of a nonregular semimontone Q-matrix

In their paper, Aganagic and Cottle gave necessary and sufficient conditions for a P0-matrix to be a Q-matrix. In his paper, Pang showed that a similar characterization for an L-matrix. In this paper, the authors show that a similar characterization for an E0-matrix (semimonotone or L1-matrix) is not possible. This is done by providing a counterexample to the inclusion E0ℝQℝR0, thus answering in the negative a question first posed by Pang.