A Combinatorial Formula for Powers of $3 \times 3$ Matrices and some Combinatorial Identities: Naraporn Na Chanta, Penying Rochanakul

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A Combinatorial Formula for Powers of $3 \times 3$ Matrices and some Combinatorial Identities

Naraporn Na Chanta, Penying Rochanakul

Authors

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Keywords:

Power matrix, Combinatorial identities

Abstract

In this paper, we give a closed-form expression for the entries of powers of a $3\times3$ matrix. This formula represents each entries of the power matrix as sum of products of the entires of the original matrix. We derive some combinatorial identities using this formula.

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Published

2020-03-01

How to Cite

Team, S. (2020). A Combinatorial Formula for Powers of $3 \times 3$ Matrices and some Combinatorial Identities: Naraporn Na Chanta, Penying Rochanakul. Thai Journal of Mathematics, 18(1). Retrieved from https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1003