Riesz representation theorem

For every continuous linear functional $f$ on a Hilbert space $\mathscr{H}$, there is a unique $u\in \mathscr{H}$ such that $f(x)=⟨x,u⟩$ for all $x\in \mathscr{H}$.
Note: $⟨x,u⟩$ denotes the inner product between $x$ and $u$.