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Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \times n$ square matrices combining ``\emph{Strassen-like}'' fast matrix multiplication approach with computational complexity $\Theta{n^{\log_2 7}}$, and ``\emph{standard}'' matrix multiplication algorithms with computational complexity $\Omega\left(n^3\right)$.
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