$\left< u, v\right> \stackrel{?}{=} \left< v, u \right>$

Question

For some vector space $V$, is it true that

$$ \left< u, v \right> = \left< v, u \right> $$

for all $u, v \in V$? Does this only hold if $V \subseteq \mathbb{R}^n$ or if $V \subseteq \mathbb{C}^n$ as well?