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March 29, 2017

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show that if u (dot) v = 0 for all vectors v, then u = 0.

One of the Axioms an inner product has to satisfy is:

x dot x >=0 where equality only holds if x = 0

So, in your problem you take the special case v = u. Then:

u dot u = 0 ---->

u = 0

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