The Wigner-Eckart theorem states ⟨j'm'|T^k_q|jm⟩ = ⟨jk;mq|j'm'⟩·⟨j'‖T^k‖j⟩, factoring matrix elements into a geometric part (Clebsch-Gordan coefficient) and a reduced matrix element. Selection rules Δm=q, |j−k| ≤ j' ≤ j+k follow automatically.