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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.