Let $H$ be a Hilbert space and let y be an element of $H-{0}$. Let $S$ be the linear span of $y$.
How can we show that the orthogonal complement of $\{x\in H:\langle x,y\rangle=0\}$ is $S$?
Let $H$ be a Hilbert space and let y be an element of $H-{0}$. Let $S$ be the linear span of $y$.
How can we show that the orthogonal complement of $\{x\in H:\langle x,y\rangle=0\}$ is $S$?