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We study the eigenvalue problem for the discrete Fourier transform (DFT) and the recently introduced collapsed DFT (CDFT). For the CDFT we in certain cases compute its symmetric rank, show it is not orthogonally decomposable, and compute its eigenvalues and eigenvectors. We generalize the theory of eigenvalues and eigenvectors for symmetric tensors to tensor products of symmetric tensors and apply this to the DFT.

Discrete Fourier transform tensors and their eigenvalues