Difference between revisions of "Pullback norm"

Revision as of 03:55, 8 March 2015 (view source) Alec (Talk | contribs) (Created page with "==Definition== Suppose we have a normed vector space, <math>(V,\|\cdot\|_V,F)</math> and another vector space {{M|(U,F)}} and a Linear map|linear i...")		Revision as of 07:23, 27 April 2015 (view source) Alec (Talk | contribs) m Newer edit →
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	{{Definition|Linear Algebra}}		{{Definition|Linear Algebra}}
−	{{Theorem|Linear Algebra}}	+	{{Theorem Of|Linear Algebra}}

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Revision as of 07:23, 27 April 2015

Definition

Suppose we have a normed vector space,

$$(V,\|\cdot\|_V,F)$$ and another vector space $(U,F)$ and a linear isomorphism $$L:(U,F)\rightarrow (V,\|\cdot\|_V,F)$$

Then we can use the norm on $V$ to "pull back" the idea of a norm into $U$

That norm is:

$$\|x\|_U=\|L(x)\|_V$$

Proof

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TODO:

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