On Sat, 10 May 2008 10:50:37 -0700 (PDT), SneakyElf@[EMAIL PROTECTED]
wrote:
>ok, here's the problem.. prove <u,v> = 0 iff ||u|| less than or equal
>to ||u + av||
>where u,v in V and a is in F.
The way you state this it's false. What's true is this:
Given u,v in V, <u,v> = 0 if and only if ||u|| <= ||u + av||
for _every_ a in F.
That should help with the proof: Supposing that
<u,v> <> 0, expand ||u+av||^2 the way you did,
and now show that there _exists_ an a such
that ||u+av|| < ||u||.
(Hint: Look for the _minimum_ of ||u+av||...)
David C. Ullrich
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