View source for Inner product/Infobox

{{Infobox
|title=Inner product
|above=<span style="font-size:2em;">{{M|\langle\cdot,\cdot\rangle:V\times V\rightarrow\mathbb{F} }}</span><br/>Where {{M|V}} is a [[vector space]] over the [[field]] {{M|\mathbb{F} }}<br/> {{M|\mathbb{F} }} may be {{M|\mathbb{R} }} or {{M|\mathbb{C} }}. 
|header1=[[subtypes of topological spaces|relation to other topological spaces]]
|label1=''is a''
|data1=<nowiki/> 
* [[topological space]]
* [[metric space]]
* [[normed space]]
|label2=''contains all''
|data2=<nowiki/>
''(none)''
|header3=Related objects
|label3=Induced [[norm]]
|data3=<nowiki/>
* {{M|1=\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:V\rightarrow\mathbb{R}_{\ge 0} }}
* {{M|1=\Vert\cdot\Vert_{\langle\cdot,\cdot\rangle}:x\mapsto\sqrt{\langle x,x\rangle} }}
For {{M|V}} a [[vector space]] over {{M|\mathbb{R} }} or {{M|\mathbb{C} }}
|label4=Induced [[metric]]
|data4=<nowiki/>
* {{M|1=d_{\langle\cdot,\cdot\rangle}:V\times V\rightarrow\mathbb{R}_{\ge 0} }}
* {{M|1=d_{\langle\cdot,\cdot\rangle}:(x,y)\mapsto\sqrt{\langle x-y,x-y\rangle} }}<br/>
:(As every [[metric induced by norm|metric induces a norm]])
For {{M|V}} considered as a [[set]]<br/>

}}