Completely- matrices

A matrix is a real square matrixM such that for everyq the linear complementarity problem: Findw andz satisfyingw = q + Mz, w ≥ 0, z ≥ 0, wTz = 0, has a solution. We characterize the class of completely- matrices, defined here as the class of-matrices all of whose nonempty principal submatrices are also-matrices.