Pullback norm

From Maths
Revision as of 16:30, 23 August 2015 by Alec (Talk | contribs) (Reverted edits by JessicaBelinda133 (talk) to last revision by Alec)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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: