On some properties of P-matrix sets Original Research Article

A nonempty set %plane1D;49E; in realn×n is said to have the row-P-property if every row representative of %plane1D;49E; is a P-matrix. We show that this property is equivalent to saying that for every nonzero x in realn there is an index i with x1(Mx)1 > 0 for all Mset membership, variant%plane1D;49E;. We relate this concept to the unique solvability of certain nonlinear complementarily problems. We also show that when %plane1D;49E; is compact and has the row-P-property, there exists a vector u > 0 such that Mu > 0 for all Mset membership, variant%plane1D;49E;.