Plane rotation/Eigenvectors/Exercise

Determine the eigenvalues, eigenvectors and eigenspaces for a plane rotation ${}{\begin{pmatrix}\operatorname {cos} \,\alpha &-\operatorname {sin} \,\alpha \\\operatorname {sin} \,\alpha &\operatorname {cos} \,\alpha \end{pmatrix}}$, with rotation angle ${}\alpha$, ${}0\leq \alpha <2\pi$,

over ${}\mathbb {R}$.

Create a solution