ON CO-POSITIVE, SEMI-MONOTONE Q-MATRICES

In this paper we consider not necessarily symmetric co-positive as well as semi-monotone Q-matrices and give a set of sufficient conditions for such matrices to be R(0)-matrices. We give several examples to show the sharpness of our results. Construction of these examples is based on the following elementary proposition: If A is a square matrix of order n whose first two rows are identical and both A(11) and A(22) are Q-matrices where A(ii) stands for the principal submatrix of A obtained by deleting row i and column i from A, then A is a Q-matrix.