hermicity

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