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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. [ABSTRACT FROM AUTHOR]

In this paper, we revise the core EP inverse of a square matrix introduced by Prasad and Mohana in [12], Core EP inverse, Linear and Multilinear Algebra62(3) (2014), 792-802. Firstly, we give a new representation and a new characterization of the core EP inverse. Then, we study some properties of the core EP inverse by using a representation by block matrices. Secondly, we extend the notion of core EP inverse to rectangular matrices by means of a weighted core EP decomposition. Finally, we study some properties of weighted core EP inverses. [ABSTRACT FROM AUTHOR]

In this paper, {1}-inverses of a nilpotent matrix as well as matrices above a given nilpotent matrix under the minus partial order are characterized. [ABSTRACT FROM AUTHOR]