Due to the commutation relations [ J i , K j ] = i ϵ ϵ i j k K k , the triple (K 1, K 2, K 3) ≡ K is a vector operator and the Wigner–Eckart theorem applies for computation of matrix elements between the states represented by the chosen basis. The matrix elements of K 0 ( 1 ) = K 3 , K ± ± 1 ( 1 ) = ∓ ∓ 1 2 ( K 1 ± ± i K 2 ) ,