The Moore-Penrose inverse of a factorization

• Author(s): Patrício, Pedro
• Date: 2005
• Persistent ID: http://hdl.handle.net/1822/3237
• Origin: RepositóriUM - Universidade do Minho
• Subject(s): Matrices over rings; Von Neumann regularity; Moore-Penrose invertibility; Factorization; Separative regular rings
• Document Type: Preprint
• Language: English

Description

In this paper, we consider the product of matrices $PAQ$, where $A$ is von Neumann regular and there exist $P^{\prime }$ and $Q^{\prime }$ such that $P^{\prime }PA=A=AQQ^{\prime }$. 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.