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arXiv · 1411.4592

Companion Matrices and Their Relations to Toeplitz and Hankel Matrices

Yousong Luo·Robin Hill
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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.

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Yousong Luo, Robin Hill. 2014-11-13. Companion Matrices and Their Relations to Toeplitz and Hankel Matrices. https://arxiv.org/abs/1411.4592

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