P Matrices and Solutions to a Class of Linear Inequalities

摘要: The main results of the paper are on pairs real $n \times n$ matrices with all off diagonal elements nonpositive. Necessary and sufficient conditions established for following two important properties, proved to be equivalent, hold a pair $(A,B)$ : (i) there exists solution $\lambda \in R^n $ set linear inequalities ^t > 0$, A B 0$; (ii) inverse $( {AD_1 + BD_2 } )$ nonnegative every $D_1 $D_2 such that {D_1 D_2 positive. in terms certain being P, class principal minors complete, finite procedure constructing is also given.