1008: Covectors (Dual) Space of Vectors Space

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definition of covectors (dual) space of 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 tensors space with respect to field and k vectors spaces and vectors space over field.

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Target Context

• The reader will have a definition of covectors (dual) space of 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:
$F$: $\in \{\text{ the fields }\}$
$V$: $\in \{\text{ the }F\text{ vectors spaces }\}$
$\ast V^{\ast }$: $=L(V:F)$
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Conditions:
//

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2: Note

$V^{\ast }$ is an $F$ vectors space, because any tensors space with respect to $F$ and k vectors spaces and vectors space over $F$ is an $F$ vectors space: refer to Note for the definition of tensors space with respect to field and k vectors spaces and vectors space over field.

Of course, it is meaningless to talk about a covectors (dual) space without specifying what vectors space it is dual of.

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References

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