The W-weighted BT inverse

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.