Difference between revisions of "Pullback norm"
From Maths
m (Reverted edits by JessicaBelinda133 (talk) to last revision by Alec) |
|||
| Line 3: | Line 3: | ||
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}} | ||
| − | + | ||
| + | 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, (V,∥⋅∥V,F) and another vector space (U,F) and a linear isomorphism L:(U,F)→(V,∥⋅∥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
TODO:
