# Matrix multiplication computational complexity based on radix 2

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?

• 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? Jul 14, 2021 at 7:15
• by the way, how do you arrive at complexity 6? I can't find the same result. Jul 14, 2021 at 9:46
• 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 Jul 14, 2021 at 9:51
• 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. Jul 14, 2021 at 9:54
• I got, Radix-2 can only be used with symmetry matrices, Jul 14, 2021 at 10:37