Abstract
A general theorem concerning the spectral relationship of two non-commuting Hermitian matrices is demonstrated. Discussion and analysis of such finding leads to consider its tight connection with respect of the Hohenberg–Kohn theorem (HKT), cornerstone of DFT theory. The present analysis shows that not only HKT can be considered a particular case of the proposed theorem, but also the validity of the studied spectral relationship can be extended from quantum mechanical ground state to excited states as well.
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