[Wien] Question on EFG and eigenvectors and sugestion for the output

[Florent Boucher]

Dear Martin,
first my name is Florent, not Florence ;-)
I am not in agreement with you concerning the choice of the axis.
I will try to explain my point of view.

 From the calculation, we have the sign of all the Vii eigenvalues. So 
we have the sign of Vzz, Vyy and Vxx
Once you have the eigenvalues, you calculate the eignvectors and those 
eigenvectors can be either in one direction or in the opposite (as you 
mentioned with the s matrix).
So, it is all the time possible to define a right-handed choice of axis 
once you have ordered the eigenvalues according to | Vzz| >= |Vyy| >= |Vxx|
We will call this the set_1 for the eigenvectors and it will give a the 
set_1 of Eulerian Angles with respect to the cartesian axis.

Now you can apply the following rotation matrices that still keep the 
right-handed definition.

R2 = [ 1,0,0; 0,-1,0; 0,0,-1]
R3 = [-1,0,0; 0, 1,0; 0,0,-1]
R4 = [-1,0,0; 0,-1,0; 0,0, 1]

This will give four different possibilities of Eulerian angles but all 
will have the correct (and well define) sign for the Vii.

You can do the same for the CSA.

Finally, you will have 16 different combinations of Eulerian Angles to 
orient the EFG with respect to the CSA and all will be perfectly equivalent.

Now, if your EFG tensor have additional symmetry, etaq=0, you can 
exchange x and y and the number of eulerian angles combinations is double.

I hope I am right ...

Regards
Florent



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