The Moore-Penrose inverse of a factorization - Patrício, Pedro (2003)
In this paper, we consider the product of matrices $PAQ$, where $A$ is von Neumann regular and there exist $P^{′ }$ and $Q^{′ }$ such that $P^{′ }PA=A=AQQ^{′ }$. We give necessary and sufficient conditions in order to $PAQ$ be Moore-Penrose invertible, extending known characterizations. Finally, an application is given to matrices over separative regular rings.