(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume the inner product is the standard inner product over the complexes.

Let W=

Spanhttp://img151.imageshack.us/img151/6804/screenshot20111122at332.png [Broken]

Find an orthonormal basis for each of W and W^{perp.}.

3. The attempt at a solution

Obviously I need to use Gram-Schmidt orthogonalization here, to find the orthonormal basis.

So I've applied the process to W, and normalized each vector to get an orthonormal basis. But I'm confused here as to what I would do for W^{perp.}. Don't I use G-S on W to find W^{perp.}? Am I finding the basis of W or am I finding W^{perp.}by applying G-S, and how am I supposed to find the other one?

If my guess is correct, do I find W^{perp.}by applying G-S to W, and then the orthonormal basis is each of these vectors normalized? Then I would apply G-S to W^{perp.}and normalized each of those vectors.

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# Homework Help: Inner product space and orthonormal basis.

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