Pullback norm

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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