PERTURBING NON-REAL EIGENVALUES OF NONNEGATIVE
Thomas J. Laffey · 2005
Let A be an (entrywise) nonnegative n×n matrix with spectrum σ and Perron eigen- value ρ. Guo Wuwen (Linear Algebra and its Applications 266 (1997), pp. 261-267) has shown that if λ is another real eigenvalue of A, then, for all t ≥ 0, replacing ρ, λ in σ by ρ + t, λ − t ,r espec tively, while keeping all other entries of σ unchanged, again yields the spectrum of a nonnegative matrix. He poses the question of whether an analogous result holds in the case of non-real λ .I n this paper, it is shown that this question has an affirmative answer.