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Determinants and inverses of circulant matrices with Jacobsthal and Jacobsthal-Lucas numbers. (English) Zbl 1302.15005

Summary: Let \(n\geq 3\) and let \(\mathbb J_n=\mathrm{circ}(J_1,J_2,\dots,J_n)\) and \(\mathbb j_n = \mathrm{circ}(j_1,j_2,\ldots,j_{n-1})\), be the \(n\times n\) circulant matrices associated with the Jacobsthal numbers \(J_1,\dots,J_n\) and the Jacobsthal-Lucas numbers \(j_1,\ldots,j_{n-1}\), respectively. The determinants and the inverses of \(J_{n}\) and \(j_{n}\) are obtained in terms of \(J_1,\dots,J_n\) and \(j_1,\ldots,j_{n-1}\), respectively.

MSC:

15A09 Theory of matrix inversion and generalized inverses
15B36 Matrices of integers
15A15 Determinants, permanents, traces, other special matrix functions
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