If the differential operator L can be factored as L = L 1 L 2 then the Green's function of L can be constructed from the Green's functions for L 1 and L 2 : G ( x , s ) = ∫ ∫ G 2 ( x , s 1 ) G 1 ( s 1 , s ) d s 1 . The above identity follows immediately from taking G ( x , s ) to be the representation of the right operator inverse of L , analogous to how for the invertible linear operator C , defined by C = ( A B ) − − 1 = B − − 1 A − − 1 , is represented by its matrix elements C i , j .