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arXiv · 1512.07025

Determinants Containing Powers of Generalized Fibonacci Numbers

Aram Tangboonduangjit·Thotsaporn Thanatipanonda
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Abstract

We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These studies have led us to discover a fundamental identity of determinant involving powers of linear polynomials. Finally, we discuss the determinants of matrices whose entries are products of the generalized Fibonacci numbers.

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Aram Tangboonduangjit, Thotsaporn Thanatipanonda. 2016-07-30. Determinants Containing Powers of Generalized Fibonacci Numbers. https://arxiv.org/abs/1512.07025

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