2024-04-14

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

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

Topics


About: vectors space

The table of contents of this article


Starting Context



Target Context


  • The reader will have a definition of affine combination of possibly-non-affine-independent set of base points on real 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:
\( V\): \(\in \text{ the real vectors spaces }\)
\( \{p_0, ..., p_n\}\): \(\subseteq V\), \(\in \{\text{ the possibly-non-affine-independent sets of base points on } V\}\)
\(*p\): \( = \sum_{j = 0 \sim n} t^j p_j \in V\), \(t^j \in \mathbb{R}\)
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Conditions:
\(\sum_{j = 0 \sim n} t^j = 1\)
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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 \(t^j \in \mathbb{R}, \sum_{j = 0 \sim n} t^j = 1\)


References


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