As I am pretty sure that everybody knows that a Hilbert space is a space that is a complete, separable and generally infinite dimensional inner product space. By the means of completion, every Cauchy sequence is convergent in this space. Besides, every inner product space is a normed space which is also a metric space, that can be shown as folows:
$d(\vec{x}, \vec{y})=\| \vec{x}-\vec{y}\| $
However, in a document online, I just saw this notation below which I can not understand.
$d(\vec{x}, \vec{y})=\| \vec{x}-\vec{y}\| =\sqrt{\langle \vec{x}, \vec{y}\rangle} $
How can the third part of this equality above hold? Thanks in advance.