Normal operator

Normal operators are defined as those operator wich commutes with their hermitian adjoint:

$[N,N^{\dagger }]=N\,N^{\dagger }-N^{\dagger }\,N=0$

where $[\,]$ denote the commutator also called the Lie bracket
and $N^{\dagger }$ denote the hermitian adjoint of $N$

Exemple of normal operators:

• Unitary operators ($N^{\dagger }=N^{-1}$)
• Hermitian operators ($N^{\dagger }=N$)

See also:

• normal matrix
• spectral theorem