RT info:eu-repo/semantics/article
T1 On universal realizability of spectra
A1 Julio, Ana I.
A1 Marijuán López, Carlos
A1 Pisonero Pérez, Miriam
A1 Soto, Ricardo L.
K1 Nonnegative matrices
K1 Matrices no negativas
K1 Eigenvalue problem
K1 Problema de valor propio
AB 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 listΛ is said to be universally realizable (UR) if it is the spectrum of anonnegative matrix for each possible Jordan canonical form allowed byΛ. It is well known that an n × n nonnegative matrix A is co-spectralto a nonnegative matrix B with constant row sums. In this paper, weextend the co-spectrality between A and B to a similarity between Aand B, when the Perron eigenvalue is simple. We also show that ifǫ ≥ 0 and Λ = {λ1, λ2, . . . , λn} is UR, then {λ1 + ǫ, λ2, . . . , λn} is alsoUR. 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 URimplies Λ1 ∪ Λ2 is UR.
PB Elsevier
SN 0024-3795
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/35977
UL http://uvadoc.uva.es/handle/10324/35977
LA eng
NO Linear Algebra and its Applications, 2019, vol. 563. p. 353-372
NO Producción Científica
DS UVaDOC
RD 23-abr-2024