Co-NP-completeness of some matrix classification problems

The classes of P-, P 0-, R 0-, semimonotone, strictly semimonotone, column suucient, and nondegenerate matrices play important roles in studying solution properties of equations and complementarity problems and conver-gence/complexity analysis of methods for solving these problems. It is known that the problem of deciding whether a square matrix with integer/rational entries is a P-(or nondegenerate) matrix is co-NP-complete. We show, through a uniied analysis, that analogous decision problems for the other matrix classes are also co-NP-complete.