A note on E′-matrices

✍ Scribed by R.A. Danao

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 433 KB
• Volume: 259
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(96)00294-7

✦ Synopsis

Let E* denote the class of square matrices M such that the linear complementarity problem Mz + q > 0, z > 0, (Mz + q) TV = 0, has a unique solution for every q such that 0 # q > 0. We show that E' g E* \ E, where E is the strictly semimonotone matrices, consists of completely Q. matrices whose proper principal submatrices are completely Q matrices. We also show that (1) singular P,-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 I',-matrices that are not Q-matrices.