Operator matrix representations of the Generalised Bott–Duffin Inverse

In this paper, we give the operator matrix representation of the generalised Bott–Duffin inverse A† (M,N) = P M,N (AP M,N + P N,M)† using results that concern lower-triangular operator matrices. Specially, we extend some previous results and we give necessary and sufficient conditions for A† (M,N) = (P M,N AP M,N)† to hold.