Drazin inverses and their modern generalisations constitute a pivotal area of operator theory within Banach algebras. These inverse concepts extend the classic notion of the matrix inverse to settings ...

In this article, we study the forward order laws for {1, 2, 3}- and {1, 2, 4}-inverses of a product of three matrices by using the maximal and minimal ranks of the generalized Schur complement. The ...

Abstract. In this paper, we present the explicit expression for the group inverse of the sum of two matrices. As an application, the explicit expression for the group ...

Banach spaces, as complete normed vector spaces, form the backbone of modern functional analysis and provide the setting for analysing a wide range of linear operators. Generalised inverses extend the ...