1130: Top-Covectors Space of Finite-Dimensional Vectors Space

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definition of top-covectors space of finite-dimensional 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: Note

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Starting Context

• The reader knows a definition of antisymmetric tensors space with respect to field and $k$ same vectors spaces and vectors space over field.

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Target Context

• The reader will have a definition of top-covectors space of finite-dimensional 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:
$F$: $\in \{\text{ the fields }\}$
$V$: $\in \{\text{ the }d\text{ -dimensional }F\text{ vectors spaces }\}$
$\ast {\mathrm{\Lambda }}_d(V:F)$:
//

Conditions:
//

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2: Note

${\mathrm{\Lambda }}_d(V:F)$ is $1$-dimensional, by the proposition that the antisymmetric tensors space with respect to any field and any $k$ same finite-dimensional vectors spaces over the field and the field has the basis that consists of the wedge products of the increasing elements of the dual basis of the same vectors space.

Each element of ${\mathrm{\Lambda }}_d(V:F)$ is called "top-covector".

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References

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