Pullback norm

From Maths
Revision as of 03:55, 8 March 2015 by 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...")

(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:


Linear Algebra