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.
@article{bwmeta1.element.doi-10_1515_spma-2015-0021,
author = {Yousong Luo and Robin Hill},
title = {Companion matrices and their relations to Toeplitz and Hankel matrices},
journal = {Special Matrices},
volume = {3},
year = {2015},
zbl = {1327.15024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0021}
}
Yousong Luo; Robin Hill. Companion matrices and their relations to Toeplitz and Hankel matrices. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0021/
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