Difference between revisions of "Pullback norm"
From Maths
(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...") |
(No difference)
|
Revision as of 03:55, 8 March 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:
Linear Algebra
