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Gram Schmidt Orthonormalization 
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#1
Oct2604, 09:48 PM

P: 80

So I'm to show that the nonzero vector w={v e V<v,x> = 0} for all x in V that dim(w)=dim(V)1.
It recommends using the GramSchmidt process to prove this but I tried to work it out and I couldn't make any sense of it. Any suggestions on how to start this out? [edit]: nevermind, I got it. If you were curious, start by saying x is an element of the set S that is linearly independent and spans V. Then do GS on V and you find that you lose an element of the set, so there you have it. 


#2
Oct2704, 08:50 AM

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PF Gold
P: 39,495

I think what you mean to say is "prove that the subspace consisting of all vectors v such that <v, x>= 0 (where x is nonzero) has dimension dim(V) 1."
Select a basis for V containing x and perform a "GramSchmidt" starting the process with x as the first vector (so GramSchmidt will give a basis containing one basis vector in the same direction as x). 


#3
Oct2704, 11:35 PM

P: 80

That's definitely what I meant, but I copied it verbatim from my crappy book (Messer's Linear Algebra) starting with "show the vector . . ." It's good with proofs, not so good with the math.



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