To address @timhoffm's other comment ("Does it still make sense to keep Affine2D._mtx as a numpy array if we only do element-wise operations?"): I'm quite convinced the whole transform stack would be faster if the transformation matrix was not a numpy array (because 3x3 is a size where the numpy's overhead is generally bigger than the gains from vectorization), but changing everything at once (even better would be to move things to C, but using plain C structs (or equivalently C++ objects) to store the coefficients) would be quite a big PR. So I'm doing the easy parts first :-)

Originally posted by @anntzer in #22119