Hi. My class notes define ( grad u ) like this :
(all the x are tensor products, and the d's are partial derivatives)

grad u = del x u
= (du/dxq) x eq
= (d/dxq)(upep) x eq
= (dup/dxq) ep x eq

where u is a vector function of x, and {ei} are basis vectors.

I'm confused about how the eq is put on the right hand side of the tensor product - seems to me it should be on the left, since it's associated with del, and not u.
That is, I think it should be:

del x u
= eq d/dxq x upep
= (dup/dxq) eq x ep

i.e. with ep and eq the other way around to my notes. This is also how my textbook seems to define it.

So my question is, does the order of ep and eq make a difference? It seems to me it would result in a different matrix (the transpose??), but I'm not sure.
If they're different, which definition is correct?