plz give the proof of "mobius transformation corresponds to a rotation of the Riemann sphere if and only if it corresponds a unitary matrix"
i shall be very thankful
There's a simple way to do this. Remember that rotations of the plane correspond to unitary matrices.
Consider now the Riemann sphere and the projection map .
If is a rotation of the sphere, for a fixed point let .
The two points lie on the complex plane, so a rotation of the plane exists
such that . Since was randomly chosen, we have .
So, the map corresponds to a unitary matrix, as required.