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eigenvalues of matrices or operators

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Characterizing the singular values of a matrix with structure

$$X=\lbrace{0,\ldots,n-1\rbrace}$$ $$Y=\lbrace{-K,-K+\Delta K,\ldots,K\rbrace}, 0< K \le T$$ $$\Delta K=\frac{2K}{m-1}$$ Is it possible to characterize the singular values of $\mathbf{F}$ or the eigenvalues
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