- #1
Oster
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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.
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.
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.