Companion Matrices and Their Relations to Toeplitz and Hankel Matrices
General Mathematics
2014-11-18 v1
Abstract
In this paper we describe some properties of companion matrices and demonstrate some special patterns that arise when a Toeplitz or a Hankel matrix is multiplied by a related companion matrix. We present a new condition, generalizing known results, for a Toeplitz or a Hankel matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.
Keywords
Cite
@article{arxiv.1411.4592,
title = {Companion Matrices and Their Relations to Toeplitz and Hankel Matrices},
author = {Yousong Luo and Robin Hill},
journal= {arXiv preprint arXiv:1411.4592},
year = {2014}
}