  This appendix to the paper by Werpachowska and Dietl "Theory of spin waves in
ferromagnetic (Ga,Mn)As" (DOI: 10.1103/PhysRevB.82.085204) is a response to
inquiries about the derivation of the Loewdin calculus and its numerical
implementation. It presents the detailed version of the Loewdin calculus for
the multiband Hamiltonian taking into account both the p-d and s-d exchange
couplings. This should explain how to implement the sp-d exchange interaction
in the tight-binding computational scheme. I also include the complete
procedure of the Bogoliubov transform for systems with spatial inversion
asymmetry.
