On universal realizability of spectra
Publication date: Available online 9 November 2018
Source: Linear Algebra and its Applications
Author(s): Ana I. Julio, Carlos Marijuán, Miriam Pisonero, Ricardo L. Soto
A list 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 () if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by Λ. It is well known that an 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 and is then is also . We give counter-examples for the cases: is implies is and are implies is .