On some classes of matrices related to solving linear complementarity problems as linear programs

A characterization of the class of hidden Markowski matrices is established. As a consequence of this, two classes of matrices belonging to the hidden Minkowski class are identified. A sufficient condition under which a hidden Z-matrix will have all its principal minors nonnegative is given. This is a generalization of a similar result for Z-matrices observed by Fiedler and Ptak. Some properties of the class of hidden Z-matrices having nonnegative principal minors are investigated.