Review

The W -weighted BT inverse

Published in: Quaestiones Mathematicae
Volume 46 , issue 2 , 2023 , pages: 359–374

DOI: 10.2989/16073606.2021.2014596

Author(s): D.E. Ferreyra Universidad Nacional de Río Cuarto, Argentina , N. Thome Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Spain , C. Torigino Universidad Autónoma de Entre Ríos, Argentina

Keywords: 15A09 , Weighted generalized inverses , W -weighted BT inverse , W -weighted core EP inverse , W -weighted Drazin inverse

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Abstract

In this paper we extend the definition of BT inverse of square complex matrices to rectangular matrices. This new generalized inverse (called the W -weighted BT inverse) always exists and is unique. We investigate several characterizations of the W -weighted BT inverse. We give two representations of the W -weighted BT inverse; the first one uses the weighted core EP decomposition and the second one is given in terms of a singular value decomposition. In addition, we derive some properties of the W -weighted BT inverse and its relationship with others well-known inverses.

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