## 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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### References:

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