Bounds for the greatest characteristic root of an irreducible nonnegative matrix II

AbstractThis paper is a continuation of our paper [3] in Linear Algebra Appl. Another new lower bound for the Perron root ω of an irreducible nonnegative matrix A is obtained. It improves the bound of Frobenius [4] that ω is greater than the greatest main diagonal element. In particular, if A is symmetric, then ω is greater than the sum of the greatest element of A plus the arithmetic mean of the two smallest main diagonal elements