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Math Help - Inner product proof

  1. #1
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    Inner product proof

    I could use some help on this proof...

    Suppose u,v\in V. Prove that <u,v>=0 if and only if ||u||\leq ||u+av|| for all a\in F.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by zebra2147 View Post
    I could use some help on this proof...

    Suppose u,v\in V. Prove that <u,v>=0 if and only if ||u||\leq ||u+av|| for all a\in F.
    What do you think? And, I assume that the norm is the natural one induced by the inner product.
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  3. #3
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    Well, I'm guess that we are going to use the fact that since <u,v>=0 then u,v are orthogonal. Then, we can evaluate the norm of u+v. That is, ||u+v||. Then, we can use Pythagorean Theorem to show that ||u||^2\leq ||u+v||^2. Then, the proof the other way would probably be similar???
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