definition of normed vectors space
Topics
About: vectors space
The table of contents of this article
Starting Context
- The reader knows a definition of %field name% vectors space.
- The reader knows a definition of norm on real or complex vectors space.
Target Context
- The reader will have a definition of normed vectors space.
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: Structured Description
Here is the rules of Structured Description.
Entities:
\( F\): \(\in \{\mathbb{R}, \mathbb{C}\}\), with the canonical field structure
\( V\): \(\in \{\text{ the } F \text{ vectors spaces }\}\)
\( \Vert \bullet \Vert\): \(\in \{\text{ the norms on } V\}\)
\(*(V, \Vert \bullet \Vert)\):
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Conditions:
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2: Note
Any normed vectors space is a real vectors space or a complex vectors space, because any norm is not defined on any vectors space with any field that is not the real numbers field or the complex numbers field.
