Lower bounds for the spread of a nonnegative matrix
Roman Drnovšek · Mathematical Inequalities & Applications · 2021
Given an integer n 2 and a real number a 0 , let C n (a) be the collection of all nonnegative n n matrices A = [a i, j ] n i, j=1 such that a = min 1 i n a i,i and r(A) > a , where r(A) denotes the spectral radius of A . We prove some lower bounds for the spread s(A) of A C n (a) that is defined as the maximum distance between any two eigenvalues of A . In particular, we prove that