Fredricksen, John Thomas2019-10-102019-10-101983http://hdl.handle.net/10919/94442The class of real nxn matrices M, known as K-matrices, for t which the linear complementarity problem w-Mz=q, w≥O, z≥O, w^tz=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.iv, 39 leavesapplication/pdfen-USIn CopyrightLD5655.V855 1983.F773MatricesThesis