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My statement was as approximate as the one I was replying to. If the original statement had been "you can use FFT to implement some operations involving matrix multiplication faster" I wouldn't have taken issue with it. But saying "FFT is faster than matrix multiplication" has little meaning.

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The naive implementation of the DFT in terms of a matrix-vector multiplication has time complexity O(n^2) [1]. The point is that the FFT approach is much faster than that implementation.

[1] https://en.wikipedia.org/wiki/DFT_matrix

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