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I was wondering if anyone could help me or point me to resources to find the eigenvalue of the following infinite matrix: $g_{ij}=\text{exp}\left(\frac{-i j}{2}\right)$.

Most resources I have found have required diagonal dominance, which this matrix does not have. Thanks!

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  • $\begingroup$ What is the range of $i, j$? $\endgroup$
    – Fedor Petrov
    Commented Dec 17, 2023 at 15:49
  • $\begingroup$ both are 0 to infinity $\endgroup$
    – Ellio
    Commented Dec 18, 2023 at 21:53

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