The recursive computation of the entries of integer powers of a companion matrix are extended to the general case of an infinite-type matrix and the possibility to compute matrix functions of a companion matrix by using the Dunford-Taylor integral is shown.
"A note on integer powers of a companion matrix and applications." Tbilisi Math. J. 13 (4) 103 - 111, December 2020. https://doi.org/10.32513/tbilisi/1608606052