Hermicity

English

Noun

1. The quality that an operator has of being Hermitian.

   Unitarity is to hermicity what orthogonality is to symmetry. (That is, conjugation by unitary matrices preserves a Hermitian matrix’s hermicity, just as conjugation by orthogonal matrices preserves a symmetric matrix’s symmetry: $(OS{O}^{-1}{)}^T=(OS{O}^T{)}^T=O^{TT}{S}^T{O}^T=OS{O}^T=OS{O}^{-1}$; $(UH{U}^{-1}{)}^{†}=(UH{U}^{†}{)}^{†}=U^{††}{H}^{†}{U}^{†}=UH{U}^{†}=UH{U}^{-1}$.