Provided the transformation from Eq. 3-36 the individual components of the Jacobi matrix can be calculated as:

In this case, the Jacobi matrix can be written as:

The inverse (reciprocal) Jacobi matrix [J]^{-1} only exists if [J] is non-singular, i.e. the determinante of the Jacobi matrix is unequal to zero for each point of the master element [*1]:

Altogether it can be stated that the transformation has to be continuous, differentiable and invertible. At the same time it should be relatively simple, so that the Jacobi matrix can be calculated with little effort.