A definition of derivative of normed vectors spaces map
Topics
About: vectors space
The table of contents of this article
Starting Context
- The reader knows a definition of normed vectors space.
- The reader knows a definition of map.
Target Context
- The reader will have a definition of derivative of normed vectors spaces map.
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.
Main Body
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 \(\lim_{\Vert v_{12} \Vert \to 0} \frac{\Vert r \Vert}{\Vert v_{12} \Vert} = 0\)
