I need help with the following problem:
Let $H\subseteq\mathbb R^3$ be a plane with cartesian equation $x=y,$ and let $r$ be the straight line generated by $(1,1,2)$. Find an endomorphism $\phi$ of $\mathbb R^3$ such that $\phi(\mathbb R^3)=H$ and $\phi^2(\mathbb R^3)=r$.
Is there a standard way to choose such endomorphism $\phi$?