By developing this concept further, one can define another operator j as the inner product of j with itself: j 2 = j x 2 + j y 2 + j z 2 . This is an example of a Casimir operator. It is diagonal and its eigenvalue characterizes the particular irreducible representation of the angular momentum algebra s o ( 3 , R ) ≅ ≅ s u ( 2 ) . This is physically interpreted as the square of the total angular momentum of the states on which the representation acts.