angles of rotation in n-dimensions

Question

What I want to do is to find $n(n-1)/2$ angles of rotation given two n-D vectors $F_1$ and $F_2$ in Matlab. I suppose that for that I should know general form of transformation matrix $T$ such that $F_2 = T*F_1$. I can construct it for 3-D, 4-D, 5-D and so on manually, but have problems with generalisation for code implementation. Is there any general form of n-D transformation matrix? Or is there another way to find $n(n-1)/2$ angles of rotation?

Answer 1

Here's a super easy way to find a rotation matrix $R$ that rotates $u$ to align with $v$ in $N$ dimensions. $R$ is unique in the sense that it does not rotate vectors outside the subspace of $u$ and $v$.