RT info:eu-repo/semantics/article
T1 Diagonalizably realizable implies universally realizable
A1 Marijuán López, Carlos
A1 Soto, Ricardo L.
K1 Spectra diagonalizably realizable
K1 Spectra universally realizable
K1 Nonnegative matrices
K1 Jordan structure
K1 12 Matemáticas
AB A spectrum Λ={λ1,…,λn} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix A. The spectrum Λ is diagonalizably realizable (DR) if the realizing matrix A is diagonalizable, and Λ is universally realizable (UR) if it is realizable for each possible Jordan canonical form allowed by Λ. In 1981, Minc proved that if Λ is the spectrum of a diagonalizable positive matrix, then Λ is universally realizable. One of the main open questions about the problem of universal realizability of spectra iswhether DR implies UR. Here, we prove a surprisingly simple result, which shows how diagonalizably realizable implies universally realizable.
PB International Linear Algebra Society
SN 1081-3810
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/79184
UL https://uvadoc.uva.es/handle/10324/79184
LA eng
NO The Electronic Journal of Linear Algebra, 2024, vol. 40, p. 382-395
NO Producción Científica
DS UVaDOC
RD 07-nov-2025