> As an optional enhancement, does transposing help here?

Yes, using the trmm transpose options could possibly help, but I am keeping the code a little bit simple for now.  A tempting optimization opportunity is that this code estimates 1-norms of products and powers of upper-triangular matrices, which involves both left- and right- multiplication by thin matrices using the Higham and Tisseur approximation.  This is currently only trmm-accelerated for right-multiplication, but it could be extended to both sides (and could probably also be sped up in non-blas ways...).  This acceleration could also extend to matfuncs other than expm (e.g. logm, sqrtm, fractional powers) which use similarity to triangular matrices in a more essential way than expm does.

> Does one actually need to explicitly make a copy of B?

After some frustration I learned that B is overwritten, so I am working around this by making a copy.  Maybe a demo of this behavior could be added to trmm tests.  In general, I think that numpy is quite copy-happy.  I would worry more if expm were faster, but it's O(N^3) so matrix copies do not affect it as badly as they would affect O(N^2) algorithms.