I am wondering, can we use Radix 2 based computational-complexity calculation for any matrix multiplication whose size is $N$ x $N$ ?? where $N$ = $2^K$ and $K > 1$ is an integer ?? Or it can only used for FFT matrix?

and if I have a unitary complex matrix whose size $2$x$2$ multiplied with a real vector $2$x$1$; in that case the complexity is 6, can I use the radix-2 to recalculate that complexity with less required operations?

  • $\begingroup$ When researching Radix-2, you'll likely have figured out that it's the symmetry of the DFT matrix that makes it possible; so, maybe you want to elaborate on where your doubts come from? $\endgroup$ Jul 14, 2021 at 7:15
  • $\begingroup$ by the way, how do you arrive at complexity 6? I can't find the same result. $\endgroup$ Jul 14, 2021 at 9:46
  • $\begingroup$ and: is this really about 2×2 matrices applied to 2-length vectors? Because you'll find that the naive DFT of size 2 is trivial, and doesn't profit from radix-2 at all, so it's not quite sure whether you're on the right track! Maybe give some context (it's always a good idea). Explain why you came to the conclusion an unitary matrix calculation would be doable using radix-2 (I think there's a lot of good thought here; your question doesn't sound like a wild guess! I just don't understand where this is coming from); for which $N$ do you really care? Give us a rough idea of the size of the $\endgroup$ Jul 14, 2021 at 9:51
  • $\begingroup$ real-world problem your tackling! Unitary matrices have a lot of nice properties, maybe there's some other approach to solving the problem that can actually be more efficient. $\endgroup$ Jul 14, 2021 at 9:54
  • $\begingroup$ I got, Radix-2 can only be used with symmetry matrices, $\endgroup$
    – Fatima_Ali
    Jul 14, 2021 at 10:37


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