In this article we obtain a general polynomial identity in k variables, where k ≥ 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 × k matrix. Finally, we use these results to derive various combinatorial identities.
INTEGERS: The Electronic Journal of Combinatorial Number Theory
Colgate University, Charles University, and DIMATIA
McLaughlin, J., & Sury, B. (2005). Powers of a matrix and combinatorial identities. INTEGERS: The Electronic Journal of Combinatorial Number Theory, 5(A13), 1-9. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/66