But my question (which wasn't about asymptotic complexity) stands: can we think about matrix multiplication as a convolution? If so, we can do pointwise multiplication sandwiched between Fourier transforms -- I don't expect it to be fast, I just expect it to be possible.
https://en.wikipedia.org/wiki/Sch%C3%B6nhage%E2%80%93Strasse...
But my question (which wasn't about asymptotic complexity) stands: can we think about matrix multiplication as a convolution? If so, we can do pointwise multiplication sandwiched between Fourier transforms -- I don't expect it to be fast, I just expect it to be possible.