Could someone explain me why, given a hilbert space, its orthogonal complement is always the one-element set containing 0, i.e.

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- May 16th 2011, 03:14 PMrusselOrthogonal complement of a Hilbert Space
Could someone explain me why, given a hilbert space, its orthogonal complement is always the one-element set containing 0, i.e.

- May 16th 2011, 03:28 PMTheEmptySet
- May 16th 2011, 03:29 PMDrexel28
- May 17th 2011, 02:25 AMrussel
Drexel, I think the question (b) concerns me. I suppose I must use something that has to do with the completeness of the hilbert space. But I guess TheEmptySet's answer is ok.

For example, I need this property when I want to prove that if S is a nonempty set, dense in an inner-product space X, then . - May 17th 2011, 11:18 AMDrexel28