Oops, yep. I initially had the tensor diagrams for that multiplication the other way around (vector then matrix). I changed them to be more conventional, but forgot that. As you say you can just move the tensors any which way and get the same answer so long as the connectivity is the same, though it would be Ab=bTAT or yi=∑jAijbj=∑jbjAij=∑jbjATji to keep the legs connected the same way.
Oops, yep. I initially had the tensor diagrams for that multiplication the other way around (vector then matrix). I changed them to be more conventional, but forgot that. As you say you can just move the tensors any which way and get the same answer so long as the connectivity is the same, though it would be Ab=bTAT or yi=∑jAijbj=∑jbjAij=∑jbjATji to keep the legs connected the same way.