In this paper we investigate the inheritance of certain structures under generalized matrix inversion. These structures contain the case of rank structures, and the case of displacement structures. We do this in an intertwined way, in the sense that we develop an argument that can be used for deriving the results for displacement structures from thoses for rank structures. We pay particular att...

The concept of an inverse of a singular matrix seems to have been first introduced by Moore [1], [2] in 1920. Extensions of these ideas to general operators have been made by Tseng [3], [4], [5], but no systematic study of the subject was made until 1955 when Penrose [6], [7], unaware of the earlier work, redefined the Moore inverse in a slightly different way. About the same time one of the au...

We consider the problem of characterizing nonnegativity of the Moore-Penrose inverse for matrix perturbations of the type A − XGY, when the Moore-Penrose inverse of A is nonnegative. Here, we say that a matrix B = (b ij ) is nonnegative and denote it by B ≥ 0 if b ij ≥ 0, ∀i, j. This problemwasmotivated by the results in [1], where the authors consider an M-matrix A and find sufficient conditio...

We propose an adaptation of the partitioning method for determination of the Moore–Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (rep...

In this paper, {α, k}-group periodic matrices are introduced and analyzed. Using different approach (as {1}-inverses, Moore-Penrose inverse, elementary matrices, left and right inverses and singular value decomposition) we characterize this kind of matrices. Some results presented are an extension of those known about group inverse and group periodic matrices. Key–Words:Generalized inverse, gro...

We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MPinvertible and well-supported elements. We present an algebraic proof of the reverse order rule for the MP-inverse valid under certain conditions on MP-invertible elements. Applications to C∗-algebras are given. 2000 Mathematics Subject Classification: 46L...

This article establishes a few sufficient conditions of the forward-order law for core inverse elements in rings with involution. It also presents weighted and triple inverse. Additionally, we discuss hybrid involving different generalized inverses like Moore–Penrose inverse, group

The reverse order rule (AB)† = B†A† for the Moore-Penrose inverse is established in several equivalent forms. Results related to other generalized inverses are also proved.