Companion unit lower Hessenberg matrices
Spectral Theory
2020-01-20 v1 Rings and Algebras
Abstract
In recent years there has been a growing interest in companion matrices. There is a deep knowledge of sparse companion matrices, in particular it is known that every sparse companion matrix can be transformed into a unit lower Hessenberg matrix of a particularly simple type by any combination of transposition, permutation similarity and diagonal similarity. The latter is not true for the companion matrices that are non-sparse, although it is known that every non-sparse companion matrix is nonderogatory. In this work the non-sparse companion matrices that are unit lower Hessenberg will be described. A natural generalization is also considered.
Keywords
Cite
@article{arxiv.2001.06470,
title = {Companion unit lower Hessenberg matrices},
author = {Alberto Borobia and Roberto Canogar},
journal= {arXiv preprint arXiv:2001.06470},
year = {2020}
}