definition of orthogonal linear map
Topics
About: vectors space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of linear map.
- The reader knows a definition of normed vectors space.
Target Context
- The reader will have a definition of orthogonal linear map.
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:
\( F\): \(\in \{\mathbb{R}, \mathbb{C}\}\), with the canonical field structure
\( V_1\): \(\in \{\text{ the normed } F \text{ vectors spaces }\}\)
\( V_2\): \(\in \{\text{ the normed } F \text{ vectors spaces }\}\)
\(*f\): \(: V_1 \to V_2\), \(\in \{\text{ the linear maps }\}\)
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Conditions: \(\forall v \in V_1 (\Vert v \Vert = \Vert f (v) \Vert)\)
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2: Natural Language Description
For any \(F \in \{\mathbb{R}, \mathbb{C}\}\), with the canonical field structure, and any normed \(F\) vectors spaces, \(V_1, V_2\), any linear map, \(f: V_1 \to V_2\), such that \(\forall v \in V_1 (\Vert v \Vert = \Vert f (v) \Vert)\)
