I am a beginner in Affine Geometry and I always have problems with proving something. So I have problems with this exercise:
There are two affine subspaces $H_1$ and $H_2$ in an affine space $R^n$. I have to prove that there exists an affine map $\phi$: $R^n \rightarrow R^n$ between these two subspaces.
I follow the book "Geometry", Audin. So, first, I assume that there is a map between $H_1$ and $H_2$. Then, I have to prove that it is affine. So I think that I have to use the relation $\vec{\phi}$($\vec{OM}$) = $\vec{\phi(O)\circ\phi(M)}$, where O and M belong to $R^n$, to prove that $\phi$ is affine. But after that I am really stuck.
Please, give me a hint what to do. I know it should be trivial, but I really have no idea.