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The eigenvalues of the matrix $\Big(\frac{1}{\cos(k-l)\frac{\pi}{n}}\Big)_{k,l=1}^n$
What are the eigenvalues/eigenvectors of the matrix $A=\Big(\frac{1}{\cos(k-l)\frac{\pi}{n}}\Big)_{k,l=1}^n$ when $n$ is odd?
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