Hello, I'm solving a problem with the ellipsoid of inertia.
The ellipsoid is described by radius of gyration tensor (RGT),
which after diagonalization gives eigenvalues and within the
diagonalization I'm obtaining also eigenvectors.

Now, I'm holding RGT, eigenvalues, eigenvectors. My
question is, how it is possible to get orientation (or 3 angles
of rotation respectively) of the ellipsoid, in the
former reference system (before transformation to the
principal axes), where are the coordinates of
physical body related to.

I think the calculated matrices contain enough information,
however I can't see the angles in it.

Thank you very much for helping in advance,