Abstract
In this paper we consider not necessarily symmetric co-positive as well as semi-monotoneQ-matrices and give a set of sufficient conditions for such matrices to beR0-matrices. We give several examples to show the sharpness of our results. Construction of these examples is based on the following elementary proposition: IfA is a square matrix of ordern whose first two rows are identical and bothA11 andA22 areQ-matrices whereA ii stands for the principal submatrix ofA obtained by deleting rowi and columni fromA, thenA is aQ-matrix.
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