Prove that $\operatorname{Hom}(V,W)$ and $M_{m \times n}(F)$ are isomorphic by constructing an isomorphism $\alpha:\operatorname{Hom}(V,W) \rightarrow M_{m \times n}(F)$. (Also given that $\dim(V)=n$ and $\dim(W)=m$)
Question, when prompt says construct, does that mean give an explicit formula for $\alpha$? I'm not exactly sure how to proceed, by a theorem in my textbook, I know they are isomorphic. but how to create such a formula?