The inverse eigenvalue problem for real eventually positive matrices
Jianbiao Chen, Zhaoliang Xu · Filomat · 2007
The eventually positive inverse eigenvalue problem(EPIEP) asks when a list ? = (???2,???n) 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 ?. And a complete answer to the EPIEP prescribed the left and the right Perron eigenvectors of the realizing matrix is also given.