# Hilbert space

A Hilbert space[1] is a vector space, [ilmath](H,F)[/ilmath] (where [ilmath]F[/ilmath] is either [ilmath]\mathbb{R} [/ilmath] or [ilmath]\mathbb{C} [/ilmath]) with an Inner product $\langle\cdot,\cdot\rangle$ such that [ilmath]H[/ilmath] is complete with respect to the associated norm $\|x\|=\sqrt{\langle x,x\rangle}$