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Companion matrices and their relations to Toeplitz and Hankel matrices
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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.
Title: Companion matrices and their relations to
Toeplitz and Hankel matrices
Description:
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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