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Related papers: New characterizations of weak CMP inverses

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This paper is divided into two parts. In the first part, we develop a general method for expressing ranks of matrix expressions that involve Moore-Penrose inverses, group inverses, Drazin inverses, as well as weighted Moore-Penrose inverses…

Rings and Algebras · Mathematics 2009-09-25 Yongge Tian

We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse…

Group Theory · Mathematics 2009-03-11 Xavier Mary

This paper first introduces a new generalized inverse in Minkowski space, called the m-DMP inverse, and discusses its algebraic and geometrical properties. The second objective is to characterize the m-DMP inverse equivalently by ranges,…

Optimization and Control · Mathematics 2023-03-27 Jiale Gao , Qingwen Wang , Kezheng Zuo

The Moore-Penrose inverse is a genuine extension of the matrix inverse. Given a complex matrix, there uniquely exists another complex matrix satisfying the four Moore-Penrose conditions, and if the original matrix is nonsingular, it is…

Rings and Algebras · Mathematics 2023-08-01 Chunfeng Cui , Liqun Qi

The notion of a Moore-Penrose inverse (M-P inverse) was introduced by Moore in 1920 and rediscovered by Penrose in 1955. The M-P inverse of a complex matrix is a special type of inverse which is unique, always exists, and can be computed…

Logic in Computer Science · Computer Science 2023-09-01 Robin Cockett , Jean-Simon Pacaud Lemay

We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial…

Numerical Analysis · Mathematics 2016-10-03 Gerlind Plonka , Sebastian Hoffmann , Joachim Weickert

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…

Functional Analysis · Mathematics 2019-03-05 Dijana Mosic , Daochang Zhang

The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in…

Rings and Algebras · Mathematics 2020-07-07 V. Cabezas Sánchez , F. Pablos Romo

In this paper, by using the core EP inverse and the Drazin inverse which are two well known generalized inverses, a new class of matrices entitled core EP Drazin matrices (shortly, CEPD matrices) is introduced. This class contains the set…

Numerical Analysis · Mathematics 2025-01-14 Gholamreza Aghamollaei , Mahdiyeh Mortezaei , Dijana Mosic , Nestor Thome

In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore,…

Rings and Algebras · Mathematics 2019-02-20 Jianlong Chen , Huihui Zhu , Pedro Patricio , Yulin Zhang

Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…

In this article we present a new characterization of inverse M-matrices, inverse row diagonally dominant M-matrices and inverse row and column diagonally dominant M-matrices, based on the positivity of certain inner products.

Probability · Mathematics 2020-02-24 Claude Dellacherie , Servet Martinez , Jaime San Martin

In this paper, we introduce the notation of $E$-weighted core-EP and $F$-weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses.…

Numerical Analysis · Mathematics 2021-09-21 Ratikanta Behera , Gayatri Maharana , Jajati Keshari Sahoo

The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these…

Rings and Algebras · Mathematics 2022-05-31 Dragan S. Rakić , Martin Z. Ljubenović

A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…

Numerical Analysis · Mathematics 2026-04-02 Jeffrey Uhlmann

Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are…

Functional Analysis · Mathematics 2023-05-22 Patricia Mariela Morillas

The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…

Rings and Algebras · Mathematics 2018-09-19 Ratikanta Behera , Debasisha Mishra

There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…

Numerical Analysis · Computer Science 2018-08-03 Jeffrey Uhlmann

In this paper we introduce the generalized inverse of complex square matrix with respect to other matrix having same size. Some of its representations, properties and characterizations are obtained. Also some new representation matrices of…

Rings and Algebras · Mathematics 2025-01-22 Abdessalam Kara , Néstor Thome , Dragan S. Djordjevi'c

This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of…

Numerical Analysis · Mathematics 2024-02-16 G. Maharanaa , J. K. Sahooa , Nestor Thome