> [!NOTE] Definition ($SO_{2}(\mathbb{R})$) > The second [[Special Orthogonal Group|special orthogonal group]], denoted $SO_{2}(\mathbb{R}),$ is the set of rotations on $\mathbb{R}^{2}$ about the origin. # Properties By [[Second Special Orthogonal Group Over The Reals is Subgroup of Second Orthogonal Group Over The Reals]], $SO_{2}(\mathbb{R})$ is a subgroup of $O_{2}(\mathbb{R}).$