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• W2890189183 abstract "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 ϵ≥0 and Λ={λ1,λ2,…,λn} is UR, then {λ1+ϵ,λ2,…,λn} is also UR. We give counter-examples for the cases: Λ={λ1,λ2,…,λn} is UR implies {λ1+ϵ,λ2−ϵ,λ3,…,λn} is UR, and Λ1,Λ2 are UR implies Λ1∪Λ2 is UR." @default.
• W2890189183 created "2018-09-27" @default.
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• W2890189183 date "2019-02-01" @default.
• W2890189183 modified "2023-10-03" @default.
• W2890189183 title "On universal realizability of spectra" @default.
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• W2890189183 doi "https://doi.org/10.1016/j.laa.2018.11.013" @default.
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