SO(3) group
= SO(3) group
{c}
{title2=$SO(3)$}
The SO(3) group consists of real three-by-three <orthogonal matrices> with <determinant> one. It acts by <rotation in three dimensions>. Its <group manifold> is $\mathbb{RP}^3$, since the <Adjoint double cover from SU(2) to SO(3)> identifies antipodal points of the <three-sphere>.