definition of covectors (dual) space of vectors space
Topics
About: vectors space
The table of contents of this article
Starting Context
Target Context
- The reader will have a definition of covectors (dual) space of 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:
\( F\): \(\in \{\text{ the fields }\}\)
\( V\): \(\in \{\text{ the } F \text{ vectors spaces }\}\)
\(*V^*\): \(= L (V: F)\)
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Conditions:
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2: Note
\(V^*\) 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.
