Exercise 3.E.6

Let $f_1,...,f_n$ be a basis of $F^n$ and $v_1,...,v_n\in V$

Define $S\in L(V^n,L(F^n,V))$ where $S(v_1,...,v_n)=T$ Define $T\in L(F^n,V)$ such that

For $j\in \{1,...,n\}$
Now to prove isomorphism, we need $S$ to be injective and surjective.
If $T=0$, then $v_1=\cdots =v_n=0$ by the definition of T.
$\forall <!--\; FUNCTION\; APPLICATION\; -->T$ we can find $(v_1,...,v_n)$ such that

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