Spectra universally realizable by doubly stochastic matrices

Abstract

Abstract A list of complex numbers Λ = { λ1, . . . , λn} is said to be realizable if it is the spectrum of an entrywise nonnegative matrix, and universally realizable if there exists a nonnegative matrix with spectrum Λ for each Jordan canonical form associated with Λ. The problem of characterizing the lists which are universally realizable is called the nonnegative inverse elementary divisors problem (NIEDP). This is a hard problem, which remains unsolved. A complete solution, if any, is still far from the current state of the art in the problem. In particular, in this paper we consider the NIEDP for generalized doubly stochastic matrices, and give new sufficient conditions for the existence and construction of a solution matrix. These conditions improve those given in [ELA 30 (2015) 704-720]