Statement: V is a finite dimensional vector space with basis {ei} (i goes from 1 to n). V has a norm || || defined on it(not necessarily induced by an inner product). Let x=Ʃxiei belong to V. I want to show that ||x|| ≥ ||xiei|| for any fixed i.(adsbygoogle = window.adsbygoogle || []).push({});

I'm not entirely sure this result is correct. But i remember seeing something similar in a text a while ago.

I know all the properties of a norm but i'm not sure how to proceed. I don't know how the independence of the basis vectors will fit into the proof.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Question about Normed Linear Spaces

**Physics Forums | Science Articles, Homework Help, Discussion**