A finite characterization of K-matrices in dimensions less than four

Abstract

The class of real nxn matrices M, known as K-matrices, for t which the linear complementarity problem w-Mz=q, w≥O, z≥O, wtz=O has a solution whenever w-Mz=q, w≥O, z≥O has a solution is characterized for dimensions n<4. The characterization is finite and"practical". Several necessary conditions, sufficient conditions, and counterexamples pertaining to K-matrices are also given. A finite characterization of completely K-matrices (K-matrices all of whose principal submatrices are also K-matrices) is proved for dimensions < 4.