What do you call a maximal orthonormal set?

[quasar987]

Is there a specific name for a maximal orthonormal set in an inner product space? My professor called this a "Hilbert basis" (except the french translation of this). But wiki doesn't seem to know what a Hilbert basis is.

 

[mathboy]

It's called a Hilbert subset. All infinite-dimensional inner product spaces possesses a Hilbert set and this can be proven using Zorn's Lemma (a nice exercise).

Hilbert basis is definitely not the name, because a maximal orthonormal set of an infinite-dimensional inner product space does not necessarily generate the vector space.

 

[Ynaught?]

Or maybe try here...

http://mathworld.wolfram.com/HilbertBasis.html"

and here...

http://mathworld.wolfram.com/OrthonormalBasis.html"

 

[morphism]

mathboy is right in that a maximal orthonormal set of an arbitrary inner product space need not be a basis. However, in a Hilbert space (which, judging the flavor of your recent posts, is probably what you're working with) it is. In this case, these things are usually called Hilbert space bases or, more generally, orthonormal bases.