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I was given the following problem, and i couldn't solve it yet:

Give a bijection between the elements of SO(3) and the fractional linear transformations of the form

[tex]\varphi_{z,w}\,(u)=\frac{zu+w}{-\bar wu+\bar z}[/tex], where [tex]u\in \mathbb C\cup \{\infty\};\, z,w\in \mathbb C[/tex].

Any ideas would be highly appreciated.

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# Möbius transformations and SO(3)

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