Almost P0-matrices and the class Q.

This paper demonstrates that within the class of those n×n matrices, each of which has a negative determinant, nonnegative proper principal minors and inverse with at least one positive entry, the class of Q-matrices coincides with the class of regular matrices. Each of these classes of matrices plays an important role in the theory of the linear complementarity problem. Lastly, analogous results are obtained for nonsingular matrices which possess only nonpositive principal minors.