definition of top-covectors space of finite-dimensional vectors space
Topics
About: vectors space
The table of contents of this article
Starting Context
Target Context
- The reader will have a definition of top-covectors space of finite-dimensional 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:
\( F\): \(\in \{\text{ the fields }\}\)
\( V\): \(\in \{\text{ the } d \text{ -dimensional } F \text{ vectors spaces }\}\)
\(*\Lambda_d (V: F)\):
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Conditions:
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2: Note
\(\Lambda_d (V: F)\) 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 \(\Lambda_d (V: F)\) is called "top-covector".
