On comparison of the Perron–Frobenius eigenvalues of two ML-matrices

AbstractAn ML-matrix is a matrix where all off-diagonal elements are nonnegative. A simple inequality relating the Perron–Frobenius eigenvalues of two ML-matrices can be obtained by performing a limiting operation on an inequality by Bapat [Amer. Math. Monthly 96 (1989) 137]. We derive the new inequality as a special case of a more general result which compares the values of expressions x′Ay and λ′Bμ for ML-matrices A and B and nonnegative vectors x,y,λ,μ