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The problem of constructing an orthogonal set of eigenvectors for a DFTmatrix is well studied. An elegant solution is mentioned by Matveev in hispaper "Interwining relations between the Fourier transfom and discrete Fouriertransform, the related functional identities and beyond". In this paper, wepresent a distilled form of his solution including some steps unexplained inhis paper, along with correction of typos and errors using more consistentnotation. Then we compare the computational complexity of his method with themore traditional method involving direct application of the Gram-Schmidtprocess. Finally, we present our implementation of Matveev's method as aMathematica module.

Constructing an orthonormal set of eigenvectors for DFT matrix using Gramians and determinants