2026-04-26T07:15:54Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/359772025-03-26T19:10:03Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
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.
2019-05-08
2019-05-08
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
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