Thanks Sean for this very interesting suggestion.

At first thought, I do not think that would work for me because the four components or the matrix at a giving points are not independent and defining an explicit function, which output each of these components does not seem possible. I do plan to take a look that direction since it is something that had even crossed my mind....

In case you may find interesting, below is a great link to the research area where I am encountering this problem....

http://emlab.utep.edu/ee5390em21/Lecture%2016%20--%20Transformation%20Electromagnetics.pdf

I am looking into more complex transformations....

Thanks again for your suggestion:-)

Saliou