On elementary divisors perturbation of nonnegative matrices

An outstanding result of Guo [W. Guo, Eigenvalues of nonnegative matrices, Linear Algebra Appl. 266 (1997) 261-270] establishes that if the list Λ={λ1,λ2,…,λn} is the spectrum of an n×n nonnegative matrix, where λ1 is its Perron eigenvalue and λ2∈R, then for any t⩾0, the list Λt={λ1+t,λ2±t,…,λn} is also the spectrum of a nonnegative matrix. In this paper we extend the result of Guo to elementary divisors. In particular, if A is a nonnegative matrix with spectrum Λ then, by means of two rank one perturbations, we construct a modified matrix B, which is also nonnegative, with spectrum Λt and we explicitly provide the Jordan canonical form of B.