definition of barycenter 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 barycenter 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:
\( V\): \(\in \{\text{ the real vectors spaces }\}\)
\( \{p_0, ..., p_n\}\): \(\subseteq V\), \(\in \{\text{ the affine-independent sets of base points on } V\}\)
\( [p_0, ..., p_n]\): \(= \text{ the affine simplex }\)
\(*bary ([p_0, ..., p_n])\): \(= 1 / (n + 1) (p_0 + ... + p_n)\)
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Conditions:
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2: Natural Language Description
For any real vectors space, \(V\), any affine-independent set of base points on \(V\), \( \{p_0, ..., p_n\} \subseteq V\), and the affine simplex, \([p_0, ..., p_n]\), \(*bary ([p_0, ..., p_n]) = 1 / (n + 1) (p_0 + ... + p_n)\)
