I could use some help on this proof... Suppose . Prove that if and only if for all .
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Originally Posted by zebra2147 I could use some help on this proof... Suppose . Prove that if and only if for all . What do you think? And, I assume that the norm is the natural one induced by the inner product.
Well, I'm guess that we are going to use the fact that since then are orthogonal. Then, we can evaluate the norm of . That is, . Then, we can use Pythagorean Theorem to show that . Then, the proof the other way would probably be similar???
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