Say I have a unit square in 2D that is defined by following matrix where each column denotes a point.
$A= \begin{bmatrix} 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 \end{bmatrix}$
Now I transform A with some Jacobian $J$:
$JA=B$
where:
$B=\begin{bmatrix} 0 & 1 & 2 & 0 \\ 0 & 0 & 2 & 1 \end{bmatrix}$
My question is whether there is a solution where the deformation is distributed equally for $J$ - which I know can't be constant - and if so, how to determine it.