Hi, I have a problem identifying some 3d rotation matrices. Actually I don't know if the result can be brought on the desired form, however it would make sense from a physics point of view. My two questions are given at the bottom.

(for the physics interested: this describes Kondo effect in a quantum dot with spin-orbit interaction)

The goal is to bring H on a the form where A and B are matrices describing rotations.

For Cx=Cz=0 :

That is, H is a vector product between spin S and a spin s that has been rotated around the y-axis with angle theta.

For Cx and Cz different from 0 :

In this case the matrix cannot be direct identified as a rotation around the x,y or z axis. The questions are now:

1) can it be a rotation around another axis?

2) Is it possible to write it as where A and B are matrices describing rotations?

I would be glad if anybody has an idea about how to deal with this.