The W -weighted BT inverse

Abstract

The core-EP and BT inverses for rectangular matrices were studied recently in the literature.The main aim of this paper is to unify both concepts by means of a new kind of generalized inverse called W -weighted q-BT inverse. We analyze its existence and uniqueness by considering an adequate matrix system. Basic properties and some interesting characterizations are proved for this new weighted generalized inverse. Also, we give a canonical form of the W -weighted q-BT inverse by means of the weighted core-EP decomposition.

T-BT Inverse and T-GC Partial Order via the T-Product

“…In [20,21], we see that the BT inverse can be used to characterize the EP matrix and study matrix equations. Based on results of this paper, we will discuss characterizations of special tensors and tensor equations.…”

Parametrizing W-weighted BT inverse to obtain the W-weighted q-BT inverse

“…The following lemma allows us to find the Moore-Penrose inverse of a partitioned matrix with some of its diagonal block nonsingular. Lemma 4.2 [10]…”

“…3) Recently, the W -weighted BT inverse of A was defined in [10] as the unique matrix X = A ,W ∈ C m×n satisfying the following equations…”