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

AbstractThis paper is a continuation of an earlier one by the author. We obtain a new lower bound for the Perron root r(A) of a nonnegative n × n matrix A. 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 from [7], 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