All operators can be decomposed into hermitian and anti-hermitian components

$A=\frac{A+A^{\ast }}{2}+\frac{A-A^{\ast }}{2}$, where by construction:

• $\frac{A+A^{\ast }}{2}$ is an Hermitian Operator
• $\frac{A-A^{\ast }}{2}$ is an Anti-Hermitian Operator