I want to rotate a shape in an n dimensional space (n>3) around (about) the origin. knowing the outcome of rotation on a point like A, which is A', how can I find the rotation outcome on a point like B. i.e. we know that A is transformed to A', can we find the point to which B is transformed?
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If $A$ and $B$ are in the same orbit, then yes: use conjugation. That is, if there exists some $g\in G$ with $A^g=B$ (the action of $g$ maps $A$ to $B$) then $B^h=A^{gh}$. – user1729 Jun 28 '16 at 13:10
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Possible duplicate: http://math.stackexchange.com/questions/598750/finding-the-rotation-matrix-in-n-dimensions. – Emilio Novati Jun 28 '16 at 14:22