2015•Special MatricesOpen access

Companion matrices and their relations to Toeplitz and Hankel matrices

Yousong Luo, Robin D. Hill

Abstract

Abstract In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a 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 analysis, Matrix (chemical analysis), Algebra over a field, Pure mathematics, Levinson recursion