An orthonormal system \( S \subseteq V \) of an inner product space \( H \) is called an orthonormal basis if for every orthonormal system \(T\subseteq V\) with \(S\subseteq T\) follows \(S=T\).
Remark
- For every orthonormal system \(S\) there exists a orthonormal basis containing \(S\) (see (0x68ef1c03) )