Difference between revisions of "Pullback norm"
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Revision as of 07:23, 27 April 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:
