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I know there is a double covering map between SU(2) and SO(3) but I have no idea how I would go about proving this or showing this.

can someone point me in the right direction please?

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    @steven: Take a look at [quaternions](http://en.wikipedia.org/wiki/Quaternion) and [their relationship with rotations](http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation); that's a useful way to understand the connection between $SU(2)$ and $SO(3)$.2012-05-04

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