# Jacobean matrix

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? Also, what about the case of a tensor

Tmn = (∂xr/∂ym)(∂xs/∂yn)Trs

Is the transformation just the product of 2 Jacobeans?