[joe_the_user]

Shouldn't the solution to fast matrix multiplication be logarithms, similarly to fast scalar multiplication?

https://en.wikipedia.org/wiki/Logarithm_of_a_matrix

[PythonNut]

Perhaps surprisingly, the matrix logarithm does not satisfy log(A) + log(B) = log(AB) in general (only when AB = BA) which is why you cannot use it to "multiply by adding".

[adgjlsfhk1]

More importantly, matrix logarithms only exist for square matrices.

[xyzzyz]

That’s not that big of a problem, as you can easily reduce the problem of multiplication of rectangular matrices to multiplication of square ones.