740: Orthogonal Linear Map

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definition of orthogonal linear map

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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: Natural Language Description

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Starting Context

• The reader knows a definition of linear map.
• The reader knows a definition of normed vectors space.

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Target Context

• The reader will have a definition of orthogonal linear map.

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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:
$F$: $\in \{\mathbb{R},\mathbb{C}\}$, with the canonical field structure
$V_1$: $\in \{\text{ the normed }F\text{ vectors spaces }\}$
$V_2$: $\in \{\text{ the normed }F\text{ vectors spaces }\}$
$\ast f$: $:V_1\to V_2$, $\in \{\text{ the linear maps }\}$
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Conditions: $\mathrm{\forall }v\in V_1(\Vert v\Vert =\Vert f(v)\Vert )$
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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 $\mathrm{\forall }v\in V_1(\Vert v\Vert =\Vert f(v)\Vert )$

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References

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