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}