# Rotation matrix for a Bloch sphere

1. Jun 23, 2011

Reading about the general rotation of a single qubit, a rotation of $\theta$ in the horizontal plane and $\phi$) in the vertical plane, is given as the matrix
V( $\theta$ , $\phi$) =

cos($\theta$/2) .................-i$e^{-i \phi}$ sin($\theta$/2)

-i$e^{i\phi}$ sin($\theta$/2)...........cos($\theta$/2)

(The dots are just spacing.)
Which would make sense to me except that I do not understand why the 1/2 factor for the angle in the horizontal plane is there. Could someone explain that for me? Thanks.