"The crucial point is that two algorithms with the same asymptotic complexity may have radically different performance characteristics" OK, but this was not a

"The crucial point is that two algorithms with the same asymptotic complexity may have radically different performance characteristics" OK, but this was not a thread about the difference in constant factors, and I freely admit that constant factors matter. As I said elsewhere, twice as fast is twice as fast, there is no denying that. Strassen's algorithm does not have the same asymptotic performance as the textbook algorithm. Strassen's algorithm is faster at scale. "Yes, this effect will always eventually be overtaken by wins in asymptotic complexity, but (as is often the case when matrix multiplication is involved) the constants may be such that reaching the crossover requires such comically large inputs as to render such considerations essentially negligible." It sounds like you are confusing the best known matrix multiplication algorithm, William's algorithm, with Strassen's algorithm. Strassen's algorithm is used in practice, and depending on what sort of architecture you are on the crossover point is N being in the hundreds or the thousands (for an NxN matrix). These are not comically large, these are sizes that are seen in practice in various settings.