Generation of perturbations by means of decoupled equations and their adjoints

It is shown that the procedure introduced by Wald for constructing solutions of a coupled system of linear partial differential equations from the solution of a single equation, based on the concept of the adjoint of a linear partial differential operator, can be extended to equations involving spinor fields, matrix fields and two or more fields. Some results concerning massless spinor fields are presented and the application of the method to linear perturbations of Yang-Mills fields and of Einstein-Maxwell fields is indicated.