definition of vertex of affine simplex
Topics
About: vectors space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of affine simplex.
Target Context
- The reader will have a definition of vertex of affine simplex.
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:
\( V\): \(\in \{\text{ the real vectors spaces }\}\)
\( \{p_0, ..., p_n\}\): \(\subseteq V\), \(\in \{\text{ the affine-independent sets of base points on } V\}\)
\( [p_0, ..., p_n]\): \(= \text{ the affine simplex }\)
\(*p_j\): \(j \in \{0, ..., n\}\)
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Conditions:
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The set of the vertexes of \([p_0, ..., p_n]\) is denoted as \(Vert ([p_0, ..., p_n])\).
2: Natural Language Description
For any real vectors space, \(V\), any affine-independent set of base points, \(\{p_0, ..., p_n\} \subseteq V\), and the affine simplex, \([p_0, ..., p_n]\), any \(p_j\) where \(j \in \{0, ..., n\}\)
The set of the vertexes of \([p_0, ..., p_n]\) is denoted as \(Vert ([p_0, ..., p_n])\).
