Is there a fast way to find eigenvalues of a circulant matrix over finite field?
Thanks.
2025-01-13 02:47:26.1736736446
Quick way of finding the eigenvalues of circulant matrices over finite fields
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Wikipedia gives a simple formula for the eigenvalues in terms of the entries of the top row of the circulant matrix. The same formula works over finite fields if (for an $n\times n$ circulant matrix) you replace $e^{2\pi i/n}$ with any $n^{th}$ root of unity over the finite field, i.e. any solution of $x^n=1$ with $x\in\mathbb F_q$.