Jordan chains of $h$-cyclic matrices, II
Abstract
McDonald and Paparella [Linear Algebra Appl. 498 (2016), 145--159] gave a necessary condition on the structure of Jordan chains of $h$-cyclic matrices. In this work, that necessary condition is shown to be sufficient. As a consequence, we provide a spectral characterization of nonsingular, $h$-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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.09709
- arXiv:
- arXiv:2110.09709
- Bibcode:
- 2021arXiv211009709N
- Keywords:
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- Mathematics - Spectral Theory;
- 15A18;
- 15A20;
- 15B99