Inequalities for the Minimum Eigenvalue of Doubly Strictly Diagonally Dominant M-Matrices

Abstract

Let A be a doubly strictly diagonally dominant M-matrix. Inequalities on upper and lower bounds for the entries of the inverse of A are given. And some new inequalities on the lower bound for the minimal eigenvalue of A and the corresponding eigenvector are presented to establish an upper bound for the L1-norm of the solution x(t) for the linear differential system dx/dt=-Ax(t), x(0)=x0>0.