Powers of a matrix and combinatorial identities

James Mc Laughlin, B. Sury

Published 2018-12-29Version 1

In this article we obtain a general polynomial identity in $k$ variables, where $k\geq 2$ is an arbitrary positive integer. We use this identity to give a closed-form expression for the entries of the powers of a $k \times k$ matrix. Finally, we use these results to derive various combinatorial identities.