Yes. I wasn't quite sure if there were any implications associated with covariant versus contravariant vectors in differential geometry. Also, in the case of a tensor, I wasn't sure if the transformation was the product of the Jacobean with it's inverse or transpose.
I'm not sure if this belongs in physics or here. Consider the transformation of a vector from one coordinate system to the other. I can write:
Vn = (∂yn/∂xm)Vm - contravariant form
Vn = (∂xm/∂yn)Vm - covariant form
In each case are the partials equivalent to the Jacobean matrices...