Bounds and inequalities for the Perron root of a nonnegative matrix

In this paper, bounds and inequalities for the Perron roots of a nonnegative matrix, extending and complementing the classical theorems of Frobenius and Ostrowski in terms of (deleted) row and column sums, are presented. All the results are derived by using the same approach, based on the monotoncity property of the Perron root.