2021-10-19T06:26:57Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/359772021-06-24T07:40:41Zcom_10324_32197com_10324_952com_10324_894col_10324_32199
00925njm 22002777a 4500
dc
Julio, Ana I.
author
Marijuán López, Carlos
author
Pisonero Pérez, Miriam
author
Soto, Ricardo L.
author
2019
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.
Linear Algebra and its Applications, 2019, vol. 563. p. 353-372
0024-3795
http://uvadoc.uva.es/handle/10324/35977
https://doi.org/10.1016/j.laa.2018.11.013
On universal realizability of spectra