A note on E'-matrices

Let E* denote the class of square matrices M such that the linear complementarity problem Mt + q greater than or equal to, 0, z greater than or equal to 0, (Mt + q)(T)z = 0, has a unique solution for every q such that 0 <not equal q greater than or equal to 0. We show that E' corresponds to E*\E, where E is the strictly semimonotone matrices, consists of completely Q(0) matrices whose proper principal submatrices are completely Q matrices. We also show that (1) singular P-1-matrices are in E* and those that are in E' are U-matrices and (2) in the classes of adequate matrices and Z-matrices, the E'-matrices are precisely the singular P-1-matrices that are not Q-matrices. (C) Elsevier Science Inc., 1997.