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2019-05-08T09:13:40Z urn:hdl:10324/35977 On universal realizability of spectra Julio, Ana I. Marijuán López, Carlos Pisonero Pérez, Miriam Soto, Ricardo L. Producción Científica A list Λ = {λ1, λ2, . . . , λn} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. The list Λ is said to be universally realizable (UR) if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by Λ. It is well known that an n × n nonnegative matrix A is co-spectral to a nonnegative matrix B with constant row sums. In this paper, we extend the co-spectrality between A and B to a similarity between A and B, when the Perron eigenvalue is simple. We also show that if ǫ ≥ 0 and Λ = {λ1, λ2, . . . , λn} is UR, then {λ1 + ǫ, λ2, . . . , λn} is also UR. We give counter-examples for the cases: Λ = {λ1, λ2, . . . , λn} is UR implies {λ1 + ǫ, λ2 − ǫ, λ3, . . . , λn} is UR, and Λ1,Λ2 are UR implies Λ1 ∪ Λ2 is UR. 2019-05-08T09:13:40Z 2019-05-08T09:13:40Z 2019 info:eu-repo/semantics/article Linear Algebra and its Applications, 2019, vol. 563. p. 353-372 0024-3795 http://uvadoc.uva.es/handle/10324/35977 10.1016/j.laa.2018.11.013 eng https://www.sciencedirect.com/science/article/pii/S0024379518305366?via%3Dihub info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2019 Elsevier Attribution-NonCommercial-NoDerivatives 4.0 International Elsevier