efficiently multiply different matrices in 3-d array with different vectors?

HI,
I was not aware of the algebraic relationship.
Tx for the explanation.

For the record; the simple example I have shown can be reproduced with
Einstein's summation rule as well. While A and x tensors have
covariant (lower) indices *only*.
So using %r%  may make sense only if we have contravariant (upper)
indices as well (mixed-variant).
Just to clarify my previous post to avoid any confusion.