Let $U$ be a subspace of a finite-dimensional space inner product $V$. It is said that using $\dim U + \dim U^ \perp =n$ can be used to prove $$U^{\perp \perp} =U.$$ But I do not see the relationship. Could anyone help?
Here we define $$U^\perp = \{v\in V; (\forall u\in U) \langle u,v \rangle = 0\}.$$