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

Naraporn Na Chanta, Penying Rochanakul

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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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|