Solution
= Solution
The <dual space> is
$$
V'=\operatorname{Hom}_F(V,F),
$$
the <vector space> of <linear functionals>, with pointwise operations
$$
(\phi+\psi)(v)=\phi(v)+\psi(v),\qquad
(a\phi)(v)=a\phi(v).
$$
Given the <basis> $e_1,\ldots,e_n$, its <dual basis> consists of the coordinate <linear functionals>
$$
\boxed{f_i\!\left(\sum_{j=1}^na_je_j\right)=a_i,
\qquad f_i(e_j)=\delta_{ij}.}
$$
In particular, $\dim V'=\dim V=n$.