536: Convex Combination of Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space

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definition of convex combination of possibly-non-affine-independent set of base points on real vectors space

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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 %field name% vectors space.
• The reader knows a definition of affine-independent set of points on real vectors space.

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Target Context

• The reader will have a definition of convex combination of possibly-non-affine-independent set of base points on real vectors space.

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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:
$V$: $\in \text{ the real vectors spaces }$
$\{p_0,...,p_n\}$: $\subseteq V$, $\in \{\text{ the possibly-non-affine-independent sets of base points on }V\}$
$\ast p$: $=\sum _{j=0\sim n}{t}^j{p}_j\in V$, $t^j\in \mathbb{R}$
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Conditions:
$\sum _{j=0\sim n}{t}^j=1\wedge 0\le t^j$
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2: Natural Language Description

For any real vectors space, $V$, and any possibly-non-affine-independent set of base points, $p_0,...,p_n\in V$, any point, $p=\sum _{j=0\sim n}{t}^j{p}_j\in V$, such that $t^j\in \mathbb{R},\sum _{j=0\sim n}{t}^j=1\wedge 0\le t^j$

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References

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