Let $V$ be a finite dimensional vector space. Let $v_1 , v_2 \in V$ and $v_1 \neq 0$. I need to show that there exists a linear map $S$ such that $S(v_1) = v_2$.
I thought of using the fact that since $V$ is isomorphic to itself, there is an invertible map that maps $v_1$ to $v_2$, but this logic seems a bit backwards.
Any advice would be helpful!