A lower bound for the Perron root of a nonnegative matrix. II (Q1112134)

This paper is a continuation of part I [ibid. 101, 181-186 (1988; reviewed above)]. We obtain a new lower bound for the Perron root r(A) of a nonnegative \(n\times n\) matrix. We show that for A with at least one principal submatrix of order two, with different diagonal entries, and with at least one positive off-diagonal entry, the bound is at least as good as the one in part I, and we determine a class of nonnegative matrices for which it is essentially better. We also show that not every nonnegative square matrix is similar to a nonnegative square matrix with identical diagonal entries.