I understand that the (sole) eigenvector of a transformation that rotates a 3D shape about an axis lies along that axis.
However, are there any eigenvectors in a transformation that rotates a shape around two (or more) axis simultaneously? Like in the motion of this sphere:
https://www.youtube.com/watch?v=_AV5JinSviE
My logic tells me no, since there would be no vector that remains on its span during this kind of rotation.