Abstract

A list Λ = {λ1, …, λn} of complex numbers is said to be realizable, if it is the spectrum of an entrywise nonnegative matrix A. In this case, A is said to be a realizing matrix. Λ is said to be universally realizable, if it is realizable for each possible Jordan canonical form (JCF) allowed by Λ. The problem of the universal realizability of spectra is called the universal realizability problem (URP). Here, we study the centrosymmetric URP, that is, the problem of finding a nonnegative centrosymmetric matrix for each JCF allowed by a given list Λ. In particular, sufficient conditions for the centrosymmetric URP to have a solution are generated.