Each normalized state is a member of an orthonormal basis: A simple proof

Iman Sargolzahi and Ehsan Anjidani

Department of Physics, University of Neyshabur, Neyshabur, Iran

In a finite dimensional Hilbert space, each normalized vector (state) can be chosen as a member of an orthonormal basis of the space. We give a proof of this statement in a manner that seems to be more comprehensible for physics students than the formal abstract one.