Abstract

We say that a list Λ={λ1,λ2,…,λn} of complex numbers is realizable if it is the spectrum of an entrywise nonnegative matrix A. We say that Λ is universally realizable (UR) if Λ is realizable for each possible Jordan canonical form allowed by Λ. The universal realizability problem of spectra (URP) has been solved for certain kind of real and complex spectra, mainly spectra in the left half-plane. In this paper we look for extending the kind of spectra that are UR by given new sufficient conditions for the URP to have a solution. In particular, we show that some realizability criteria for the real and symmetric nonnegative inverse eigenvalue problem are realizability criteria for the URP as well.