hermicity

English

Noun

hermicity (uncountable)

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: $(OSO^{-1})^{T}=(OSO^{T})^{T}=O^{TT}S^{T}O^{T}=OSO^{T}=OSO^{-1}$; $(UHU^{-1})^{\dagger }=(UHU^{\dagger })^{\dagger }=U^{\dagger \dagger }H^{\dagger }U^{\dagger }=UHU^{\dagger }=UHU^{-1}$.