Linear Map Lemma

Lemma

• With $\{v_1,\dots ,v_n\}$ as a basis for Vector Space $V$
• With $\{w_1,\dots ,w_n\}\in W$
• Then, there exists a Unique $T\in \mathcal{L}(V,W)$ s.t $T(v_k)=w_k$ for each $k\in 1,\dots ,n$