# Proof of the Piola Transform

As I understand it, the relationship between the second order tensor $$\bf T$$ over a reference configuration and the same tensor in a deformed configuration $$\bf T^\prime$$ is given defined as follows:

$${\bf T} := {\bf T^\prime} \, \textrm{cof} \, {\bf F}$$

Where $$\bf F$$ is the deformation gradient. The above relation is presented as a definition without proof in every text that I've come across, but it looks like a relationship that ought to have a proof, or some intuition ought to be given for the relation.