MR2024445 Carbó-Dorca, Ramon ; Bultinck, Patrick . Analysis of a
general theorem concerning two non-commuting Hermitian matrices:
quantum mechanical implications for ground and excited states. J.
Math. Chem. 34 (2003), no. 1-2, 75--82.

A strongly application-oriented exercise in linear algebra: Two
N-dimensional Hermitian matrices A and B with no common
eigenvectors are considered. Certain mean values of their
difference/sum are positive (= two theorems), with interesting
consequences in the density-functional formalism of quantum
chemistry.