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AbstractThe nonnegative inverse eigenvalue problem is the problem of finding necessary and sufficient conditions for the existence of an entrywise nonnegative matrix A with prescribed spectrum. This problem remains open for . If the matrix A is required to be normal, the problem will be called the normal nonnegative inverse eigenvalue problem (NNIEP). Sufficient conditions for a list of complex numbers to be the spectrum of a normal nonnegative matrix were obtained by Xu Linear Multilinear Algebra. 1993;34:353–364. In this paper, we give a normal version of a rank-r perturbation result due to Rado and published by Perfect Duke Math. J. 1955;22:305–311, which allow us to obtain new sufficient conditions for the NNIEP to have a solution. These new conditions significantly improve Xu's conditions. We also apply our results to construct nonnegative matrices with arbitrarily prescribed elementary divisors.Keywords: normal nonnegative inverse eigenvalue problemAMS Subject Classification: 15A18 AcknowledgementsWe are grateful to Prof. R. Loewy and the anonymous referee for their suggestions and comments that enabled us to improve the presentation of this paper.Notes1 Supported by Fondecyt 1120180, Chile, Conicyt-PCHA/Doc.Nac./2014-63130010.
Julio et al. (Mon,) studied this question.