  Currently, it has been claimed that certain Hermitian Hamiltonians have
parity (P) and they are PT-invariant. We propose generalized definitions of
time-reversal operator (T) and orthonormality such that all Hermitian
Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are
indefinite and definite respectively. The energy-eigenstates are either E-type
(e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry
which is recently found to exist for a non-Hermitian Hamiltonian. For a
Hermitian Hamiltonian it coincides with P.
