Rank one positive sub-definite matrix classes and linear complementarity problem

In the study of Linear Complementarity Problem (LCP), it is well known that positive sub-definite matrix class play an importent roll. In this work we consider this matrix class and also its generalized and weak generalized classes and show their complete existence in rank one matrix in Rⁿ. Then we reintroduce positive sub-definite matrix and copositive matrix and check some of their properties over a proper cone K for rank one matrix as well. Finally we propose that, positive subdefinite matrix over a proper cone is also processable by Lemke´s algorithem.