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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| + | That norm is: <math>\|x\|_U=\|L(x)\|_V</math> | ||
==Proof== | ==Proof== | ||
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:
