If $V$ is a finite dimensional vector space and $\operatorname{End} V$ is the set of endomorphisms from $V$ to $V$.
Defining a map from $V^*\otimes V\rightarrow \operatorname{End} V$ by sending some element say, $f\otimes v \in V^* \otimes V$ to endomorphism whose value at $w\in V$ is $f(w)v$.
I am trying to show this map is an isomorphism between $V^* \otimes V$ and $\operatorname{End} V$. I am trying to verify it using dual basis.
If some hint can be provided, it will be a great help!