Inner product/Infobox

Inner product
$\langle\cdot,\cdot\rangle:V\times V\rightarrow\mathbb{F}$ Where $V$ is a vector space over the field $\mathbb{F}$ $\mathbb{F}$ may be $\mathbb{R}$ or $\mathbb{C}$.
relation to other topological spaces
is a	topological space metric space normed space
contains all	(none)
Related objects
Induced norm	$\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:V\rightarrow\mathbb{R}_{\ge 0}$ $\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:x\mapsto\sqrt{\langle x,x\rangle}$ For $V$ a vector space over $\mathbb{R}$ or $\mathbb{C}$
Induced metric	$d_{\langle\cdot,\cdot\rangle}:V\times V\rightarrow\mathbb{R}_{\ge 0}$ $d_{\langle\cdot,\cdot\rangle}:(x,y)\mapsto\sqrt{\langle x-y,x-y\rangle}$ (As every metric induces a norm) For $V$ considered as a set