Linear Algebra and Its Applications
Let A be an irreducible (entrywise) nonnegative n x n matrix with eigenvalues rho, lambda(2) = b + ic, lambda(3) = b ic, lambda(4), ... , lambda(n), where rho is the Perron eigenvalue. It is shown that for any t is an element of [0, infinity) there is a nonnegative matrix with eigenvalues rho + (t) over tilde, lambda(2) +t, lambda(3) + t, lambda(4), ... , lambda(n), whenever (t) over tilde >= gamma(n) t with gamma(3) = 1, gamma(4) = 2, gamma(5) = root 5 and gamma(n) = 2.25 for n >= 6. The result improves that of Guo et al. Our proof depends on an auxiliary result in geometry asserting that the area of an n-sided convex polygon is bounded by gamma(n), times the maximum area of a triangle lying inside the polygon. (C) 2014 Elsevier Inc. All rights reserved.
Wang, X., Li, C. K., & Poon, Y. T. (2016). Perturbing eigenvalues of nonnegative matrices. Linear Algebra and its Applications, 498, 3-20.