Find an orthonormal basis for the vector subspace of

Sketch of work:

Spoiler:

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- Jun 12th 2009, 06:30 PMMorganOrthonormal basis
Find an orthonormal basis for the vector subspace of

Sketch of work:

__Spoiler__: - Jun 12th 2009, 09:13 PMNonCommAlg
first, you don't need to hide your own work! second, you're right so far. now you just need to apply Gram-Schmidt process. let's give a name to the elements of the basis you found:

now find the set is an orthogonal basis for so you just need to normalize them, i.e. find

then would be an orthonormal basis for