Thanks for your detailed reply. It's a lot to digest. As I explained in another reply, my mathematics is very poor indeed. > Likewise, think of the plane orth

Thanks for your detailed reply. It's a lot to digest. As I explained in another reply, my mathematics is very poor indeed. > Likewise, think of the plane orthogonal to the axis of rotation, then points that are on that plane rotate, but they stay on that plane. Why only the orthogonal plane, I don't see how any set of points behaves differently to any other. For example the stars could be said to rotate around the earth (I know, but pretend). They don't move in relation one another though. They only change relative to the earth. I think I'm grossly misunderstanding. Does 'rotation' have a special meaning in this context? > 45-degree rotation for example has no invariant subspace because you can rotate points on a line 45 degrees and the only one that stays the same is 0,0, which you call {0}? So.. someone tried to prove that for n dimenional (odd?) spaces with n<=infinity, there is always some subspace which doesn't differ when you apply complex transformations to it? But was wrong.