Given a (orthogonal) basis $(\sigma\_n)\_{n=1,\dots,K}$ of the algebra $u(N)$, we can represent any element $U$ of the corresponding group $U(N)$ in the form


$U=e^{i\sum\_{n=1}^K\varphi\_n\sigma\_n}$.


Is it also possible to represent every element of $U(N)$ in the following form as a product of elementary (Givens) rotations


$U=\prod\_{n=1}^K e^{i\alpha\_n\sigma\_n}$ ?


Is the corresponding property given for the special orthogonal groups $SO(N)$? For SO(3) it is -- in that case, $\alpha\_i$ are the well-known Euler angles.


thanks a lot in advance,
 Robert



Representing elements of U(N) or SO(N) by elementary rotations exp(i phi_n sigma_n)
See [this paper](http://jmp.aip.org/resource/1/jmapaq/v47/i4/p043510_s1).


