A note on integer powers of a companion matrix and applications

D. Caratelli, P. E. Ricci

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. 

Tbilisi Mathematical Journal, Vol. 13(4) (2020), pp. 103-111