2014•arXiv (Cornell University)Open access

Companion Matrices and Their Relations to Toeplitz and Hankel Matrices

Yousong Luo, Robin Hill

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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Key concepts: Toeplitz matrix, Hankel matrix, Mathematics, Matrix (chemical analysis), Matrix analysis, Algebra over a field, Pure mathematics, Levinson recursion