Jordan chains of $h$-cyclic matrices, II
Spectral Theory
2021-10-20 v1
Abstract
McDonald and Paparella [Linear Algebra Appl. 498 (2016), 145--159] gave a necessary condition on the structure of Jordan chains of -cyclic matrices. In this work, that necessary condition is shown to be sufficient. As a consequence, we provide a spectral characterization of nonsingular, -cyclic matrices. In addition, we provide results for the Jordan chains corresponding to the eigenvalue zero of singular matrices. Along the way, a new characterization of circulant matrices is given.
Cite
@article{arxiv.2110.09709,
title = {Jordan chains of $h$-cyclic matrices, II},
author = {Andrew L. Nickerson and Pietro Paparella},
journal= {arXiv preprint arXiv:2110.09709},
year = {2021}
}