579: Vertex of Affine Simplex

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definition of vertex of affine simplex

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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: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of affine simplex.

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Target Context

• The reader will have a definition of vertex of affine simplex.

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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: Structured Description

Here is the rules of Structured Description.

Entities:
$V$: $\in \{\text{ the real vectors spaces }\}$
$\{p_0,...,p_n\}$: $\subseteq V$, $\in \{\text{ the affine-independent sets of base points on }V\}$
$[p_0,...,p_n]$: $=\text{ the affine simplex }$
$\ast p_j$: $j\in \{0,...,n\}$
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Conditions:
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The set of the vertexes of $[p_0,...,p_n]$ is denoted as $Vert([p_0,...,p_n])$.

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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 $Vert([p_0,...,p_n])$.

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References

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