Editing Orthonormal basis (section)

==Orthonormal system==

A set <math>S</math> of mutually orthonormal vectors in a Hilbert space <math>H</math> is called an orthonormal system. An orthonormal basis is an orthonormal system with the additional property that the linear span of <math>S</math> is dense in <math>H</math>.{{sfn | Steinwart | Christmann | 2008 | p=503}} Alternatively, the set <math>S</math> can be regarded as either ''complete'' or ''incomplete'' with respect to <math>H</math>. That is, we can take the smallest closed linear subspace <math>V \subseteq H</math> containing <math>S.</math> Then <math>S</math> will be an orthonormal basis of <math>V;</math> which may of course be smaller than <math>H</math> itself, being an ''incomplete'' orthonormal set, or be <math>H,</math> when it is a ''complete'' orthonormal set.