Difference between revisions of "Pullback norm"

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{{Definition|Linear Algebra}}
 
{{Definition|Linear Algebra}}
{{Theorem|Linear Algebra}}
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{{Theorem Of|Linear Algebra}}

Latest revision as of 16:30, 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]

That norm is: [math]\|x\|_U=\|L(x)\|_V[/math]

Proof


TODO: