# Rotation matrix around an arbitrary axis in an n-dimensional space

I have two vectors in an n-dimensional space, where n is around 500. I need to turn one vector towards the other one by a particular angel. I found rotation matrices for rotating a vector in a 3-dimensional space around an arbitrary axis, but it is not clear what the matrix is going to look like in an n-dimensional space. Any help is appreciated.

• When $n>3$, you are no longer rotating around axes. – Ivan Neretin Sep 11 at 15:44
• To expand on that comment, rotations occur in planes. It’s only in odd-dimensional spaces that you can have a fixed rotation axis. Read up on Givens rotations as a starting point. Another way to construct such a rotation is as a composition of reflections. – amd Sep 11 at 16:53