Difference between revisions of "Strong derivative/Infobox"

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(Created page with "{{Infobox |title=Strong derivative |above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{T(x_0+h)-T(x_0)}{\Vert h\Vert_X}\right)=\overbrace{L_{x_0}:X\...")
 
(Fixed some typos, still a bit of a stub!)
 
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{{Infobox
 
{{Infobox
 
|title=Strong derivative
 
|title=Strong derivative
|above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{T(x_0+h)-T(x_0)}{\Vert h\Vert_X}\right)=\overbrace{L_{x_0}:X\rightarrow Y}^\text{Linear} }}</span><br/>For two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}} and a [[mapping]] {{M|T:U\rightarrow Y}} for {{M|U}} some [[open set]] in {{M|X}}
+
|above=<span style="font-size:1.25em;">{{MM|1=\lim_{h\rightarrow 0}\left(\frac{\big\Vert f(x_0+h)-f(x_0)-df\vert_{x_0}\big\Vert_Y}{\Vert h\Vert_X}\right)}}</span><br/>For two [[normed space|normed spaces]] {{M|(X,\Vert\cdot\Vert_X)}} and {{M|(Y,\Vert\cdot\Vert_Y)}}<br/>and a [[mapping]] {{M|f:U\rightarrow Y}} for {{M|U}} [[open set|open]] in {{M|X}}<br/><br/>{{M|df\vert_{x_0}:X\rightarrow Y}} a [[linear map]] called the<br/>"''derivative of {{M|f}} at {{M|x_0}}''"
 
}}<noinclude>
 
}}<noinclude>
 
{{Stub page|This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID}}
 
{{Stub page|This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID}}
 
[[Category:Infoboxes]]
 
[[Category:Infoboxes]]
 
</noinclude>
 
</noinclude>

Latest revision as of 14:06, 13 November 2016

Strong derivative
limh0(f(x0+h)f(x0)df|x0YhX)

For two normed spaces (X,X) and (Y,Y)
and a mapping f:UY for U open in X

df|x0:XY a linear map called the
"derivative of f at x0"
(Unknown grade)
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This is just a stub, CHECK THE INFOBOX DEFINITION IS VALID