So a spherical harmonic can also be written Y ℓ ℓ m = ⟨ ⟨ n | ℓ ℓ m ⟩ ⟩ . Spherical harmonic states | m , ℓ ℓ ⟩ ⟩ rotate according to the inverse rotation matrix U ( R − − 1 ) , while | ℓ ℓ , m ⟩ ⟩ rotates by the initial rotation matrix U ^ ^ ( R ) .