Angular momentum operators are self-adjoint operators j x, j y, and j z that satisfy the commutation relations [ j k , j l ] ≡ ≡ j k j l − − j l j k = i ℏ ℏ ε ε k l m j m k , l , m ∈ ∈ { x , y , z } , where ε klm is the Levi-Civita symbol. Together the three operators define a vector operator, a rank one Cartesian tensor operator, j = ( j x , j y , j z ) . It is also known as a spherical vector, since it is also a spherical tensor operator. It is only for rank one that spherical tensor operators coincide with the Cartesian tensor operators.