Generalized inverses of a 2×2 block partitioned matrix

All kinds of generalized inverses including M+,M+XY,Mg and Md of a 2×2 block matrix M= A C B D are discussed under some conditions.The representations are all based on M(2)T,S =U(VUM)-1V since M+,M+XY,Mg and Md are actually some kinds of {2} inverses with corresponding prescribed ranges and null spaces,where U and V are full column rank and full row rank matrices respectively such that R(U)=T,N(V)=S.