On some properties of P-matrix sets

✍ Scribed by Yoon Song; M. Seetharama Gowda; G. Ravindran

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 422 KB
• Volume: 290
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(98)10228-8

✦ Synopsis

A nonempty set ~ in R "×n is said to have the row-P-property if every row representative of ~ is a P-matrix. We show that this property is equivalent to saying that for every nonzero x in N" there is an index i with xi(Mx), > 0 for all M E ~,¢. We relate this concept to the unique solvability of certain nonlinear complementarily problems. We also show that when c0 is compact and has the row-P-property, there exists a vector u > 0 such that Mu > 0 for all M E c6.