THE INVERSE EIGENVALUE PROBLEM FOR REAL EVENTUALLY POSITIVE MATRICES 9

Abstract

The eventually positive inverse eigenvalue problem(EPIEP) asks when a list σ = (ρ, λ2,..., λn) of n complex numbers is the spectrum of a real n × n eventually positive matrix. In this paper, a constructive method is presented to solve the EPIEP. Using this method, it is easy to find the realizing matrix, i.e., a real eventually positive matrix with the spectrum σ. And a complete answer to the EPIEP prescribed the left and the right Perron eigenvectors of the realizing matrix is also given. 1