A weighted core EP inverse

D.E. FERREYRA; F. E. LEVIS; N. THOME

Valencia

Workshop; International Workshop on Industrial Mathematics 2017; 2017

The core EP decomposition has been introduced for square matrices in cite{PrMo}.Our purpose is double. On the one hand, we develop a weighted core EP decomposition of a pair of rectangular matrices $(A,W)$. On the other hand, we use the previous factorization in order to introduce a new generalized inverse, namely, the weighted core EP inverse. We study its existence and uniqueness and then we provide matrix equations that this new inverse must satisfy. Finally, we derive a characterization for the weighted core EP inverse. The found results constitute an extension to rectangular matrices of the core inverse studied in cite{BaTr1} for index 1 matrices and extended in cite{BaTr2,MaTh,PrMo} for arbitrary index.