Difference between revisions of "Pullback norm"

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Then we can use the norm on {{M|V}} to "pull back" the idea of a norm into {{M|U}}
 
Then we can use the norm on {{M|V}} to "pull back" the idea of a norm into {{M|U}}
 
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yes
That norm is: <math>\|x\|_U=\|L(x)\|_V</math>
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==Proof==
 
==Proof==

Revision as of 07:44, 23 August 2015

Definition

Suppose we have a normed vector space, [math](V,\|\cdot\|_V,F)[/math] and another vector space [ilmath](U,F)[/ilmath] and a linear isomorphism [math]L:(U,F)\rightarrow (V,\|\cdot\|_V,F)[/math]

Then we can use the norm on [ilmath]V[/ilmath] to "pull back" the idea of a norm into [ilmath]U[/ilmath] yes

Proof


TODO: