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There is the basic paper of S.Winograd (http://www.sciencedirect.com/science/article/pii/0024379571900097) about 2x2 matrix multiplication.

In the proof of the main Theorem 3.1, there is a some proposition that " ... each c$^{'}_i,_j$ can be computed using only three multiplications".

I don't understand why. Please help.

Yury

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Because $\mathbf{c}' = R'\mathbf{p}$ and $R'$ contains 3 nonzero elements in each row.

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