definition of \((p, q)\)-tensors 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 \((p, q)\)-tensors 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:
\( F\): \(\in \{\text{ the fields }\}\)
\( V\): \(\in \{\text{ the } F \text{ vectors spaces }\}\)
\( V^*\): \(= \text{ the covectors space of } V\)
\( p\): \(\in \mathbb{N}\)
\( q\): \(\in \mathbb{N}\)
\(*T^p_q (V)\): \(= L (V^*, ..., V^*, V, ..., V: F)\), where \(V^*\) appears \(p\) times and \(V\) appears \(q\) times
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Conditions:
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When \(p = q = 0\), \(T^p_q (V)\) is an element of \(F\): as there is no argument, an element of \(F\) is chosen unconditionally.
