Smigoc's glue for universal realizability in the left half-plane
Spectral Theory
2023-01-30 v1
Abstract
A list of A list {\Lambda} of complex numbers is said to be realizable if it is the spectrum of a nonnegative matrix. {\Lambda} is said to be universally realizable (UR) if it is realizable for each possible Jordan canonical form allowed by {\Lambda}. In this paper, using companion matrices and applying a procedure by \v{S}migoc, is provides a sufficient condition for the universal realizability of left half-plane spectra. It is also shown how the effect of adding a negative real number to a not UR left half-plane list of complex numbers, makes the new list UR, and a family of left half-plane lists that are UR is characterized.
Keywords
Cite
@article{arxiv.2301.11398,
title = {Smigoc's glue for universal realizability in the left half-plane},
author = {Jaime H. Alfaro and Ricardo L. Soto},
journal= {arXiv preprint arXiv:2301.11398},
year = {2023}
}