[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.