# B Composition of elements of SO(4)

#### jk22

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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#### fresh_42

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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?

#### lpetrich

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.

"Composition of elements of SO(4)"

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