A nice way to look at the 4-dimensional rotation matrices SO(4) $SO_4$ is that it's universal cover is isomorphic to S^3 x $S^3 \times S^3$. The map $S^3 x \times S^3 --> SO(4) \to SO_4$ is given by left and right quaternionic multiplication by a unit vectors.
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A nice way to look at the 4-dimensional rotation matrices SO(4) is that it's universal cover is isomorphic to S^3 x S^3. The map S^3 x S^3 --> SO(4) is given by left and right quaternionic multiplication by a unit vectors. |
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