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Even Strassen can be overly expensive for reasonably sized matrices. Almost all matrix multiplication algorithms have a threshold only beyond which do they use Strassen.

Although apparently that threshold can be lowered (http://jianyuhuang.com/papers/sc16.pdf), but even then it's a matrix that's several hundred columns by several hundred rows large.

Some CS classes explicitly use Strassen to teach the realities of asymptotic vs wall-clock time complexity, challenging students to come up with a hybrid matrix multiplication algorithm that performs the fastest and switches at the best thresholds of matrix size.




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