hermicity
Noun
Meaning
hermicity (uncountable)
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:
(
O
S
O
−
1
)
T
=
(
O
S
O
T
)
T
=
O
T
T
S
T
O
T
=
O
S
O
T
=
O
S
O
−
1
{\displaystyle (OSO^{-1})^{T}=(OSO^{T})^{T}=O^{TT}S^{T}O^{T}=OSO^{T}=OSO^{-1}}
;
(
U
H
U
−
1
)
†
=
(
U
H
U
†
)
†
=
U
†
†
H
†
U
†
=
U
H
U
†
=
U
H
U
−
1
{\displaystyle (UHU^{-1})^{\dagger }=(UHU^{\dagger })^{\dagger }=U^{\dagger \dagger }H^{\dagger }U^{\dagger }=UHU^{\dagger }=UHU^{-1}}
.