I don't know why this answer is getting downvoted. This is absolutely correct. W. Miller has a paper discussing, under conditions of numerical stability, O(n^3

I don't know why this answer is getting downvoted. This is absolutely correct. W. Miller has a paper discussing, under conditions of numerical stability, O(n^3) multiplications is necessary [0]. Any algorithm that gets sub cubic runtime for matrix multiplication, like Strassen's or Coppersmith's, must sacrifice some amount of precision or stability. [0] https://epubs.siam.org/doi/10.1137/0204009 https://epubs.siam.org/doi/10.1137/0204009