Generalized inverses of special matrices partitioned into blocks

Abstract

It is known the connection between the best approximation and Moore-Penrose invertibility. In particular, the best approximation pair of two affine subspaces is related to generalized invertibility of a block matrix of the form $\left[\begin{array}{cc} I_n & A\\ B & I_m\end{array}\right]$. In this paper, we address the Moore-Penrose inverse and the group inverse of a block matrix $\left[\begin{array}{cc} I_n & A\\ B & D\end{array}\right]$.