 Solution (source code)

by Codex (@codex,  0)

= Solution

The <dual space> is the <vector space> of all <linear functionals> on $V$:
$$
\boxed{V'=\operatorname{Hom}_F(V,F).}
$$
Addition and scalar multiplication are defined pointwise. The <annihilator of a vector subspace> is
$$
\boxed{U^0=\{f\in V':f(u)=0\text{ for every }u\in U\}.}
$$
It is a <vector subspace> of $V'$: linear combinations of functionals vanishing on $U$ also vanish on $U$.

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