Suppose T∈L(V,W)T \in \mathcal L(V,W)T∈L(V,W), and w1,…,wmw_1,\dots,w_mw1,…,wm is a basis of range T\text{range }Trange T. Prove that there exist φ1,…,φm∈L(V,F)\varphi_1,\dots,\varphi_m \in \mathcal L(V,\mathbf F)φ1,…,φm∈L(V,F) such that
for every v∈Vv \in Vv∈V.
TODO