It's a beginner's question : if I consider compositions of Givens' rotations, how many should I combine to obtain the whole group, since those don't commute and hence their order is important ? Is it 6 ?
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Can you be a bit more precise? What are "Givens' rotations"? Do you want to know whether every element of ##SO(4)## can be written as a product of certain elements and of certain length? And most of all: why?
There exists an expression of SO(4) elements in terms of pairs of unit quaternions. Each quaternion has a SO(4) rotation matrix associated with it, and the two quaternions' rotation matrices are multiplied together. Those matrices are linear functions of their quaternions, much like SU(2) matrices.
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