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May 2nd, 2010, 11:44 PM   #1
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orthonogonal complement

Let B be a basis for subspace W of an inner product space V, and let z in V. Prove that z in W? if and only if <z.v>=0 for every v in B.

=> If z in W? then <z,v> = 0
by definition of orthonogonal complement, W? = {z in V: <z,v> = 0 for all v in W}
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May 3rd, 2010, 07:53 AM   #2
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Re: orthonogonal complement

Just look at the definition of a basis, and you should be there.
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complement, orthonogonal

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