A function T: V\to W is surjective if its range equals its codomain W. “onto” “For any possible output, w \in W for T \in \mathcal{L}(V,W), there is at LEAST one input T that maps Tv \to w. "
\begin{equation} \forall w \in W, \exists v \in V:Tv=W \end{equation}
map to bigger space is not surjective See map to bigger space is not surjective