23: Derivative of Normed Vectors Spaces Map

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A definition of derivative of normed vectors spaces map

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Topics

About: vectors space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition

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Starting Context

• The reader knows a definition of normed vectors space.
• The reader knows a definition of map.

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Target Context

• The reader will have a definition of derivative of normed vectors spaces map.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Definition

For any normed vectors spaces, $V_1$ and $V_2$, and any map, $f:V_1\to V_2$, the linear map at $v_{11}$, $Df(v_{11}):V_1\to V_2$, such that $f(v_{11}+v_{12})=f(v_{11})+(Df(v_{11}))(v_{12})+r(v_{11},v_{12})$ where $\underset{\Vert v_{12}\Vert \to 0}{lim}\frac{\Vert r\Vert }{\Vert v_{12}\Vert }=0$

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References

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