Weak group inverses in proper ∗-rings

2019 ◽  
Vol 19 (12) ◽  
pp. 2050238 ◽  
Author(s):  
Mengmeng Zhou ◽  
Jianlong Chen ◽  
Yukun Zhou
Keyword(s):  
Group Inverse ◽  
Complex Matrices ◽  
Weak Group ◽  
Group Inverses

In proper ∗-rings, we characterize weak group inverses by three equations. It generalizes the notion of weak group inverse, which was introduced by Wang and Chen for complex matrices in 2018. Some new equivalent characterizations for elements to be weak group invertible are presented. Furthermore, we define the group-EP decomposition. Some properties of the weak group inverse are established by the group-EP decomposition.

scholarly journals Weak group inverse

2018 ◽  
Vol 16 (1) ◽  
pp. 1218-1232 ◽  
Author(s):  
Hongxing Wang ◽  
Jianlong Chen
Keyword(s):  
Partial Order ◽  
The Other ◽  
Group Inverse ◽  
Complex Matrices ◽  
The Core ◽  
Weak Group ◽  
Square Complex

AbstractIn this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses.

scholarly journals Weighted weak group inverse for Hilbert space operators

2020 ◽  
Vol 15 (4) ◽  
pp. 709-726
Author(s):  
Dijana Mosić ◽  
Daochang Zhang
Keyword(s):  
Hilbert Space ◽  
Group Inverse ◽  
Weak Group ◽  
Hilbert Space Operators

Representations for the weak group inverse

2021 ◽  
Vol 397 ◽  
pp. 125957
Author(s):  
Dijana Mosić ◽  
Predrag S. Stanimirović
Keyword(s):  
Group Inverse ◽  
Weak Group

scholarly journals The Group Inverse of the Combinations of Two Idempotent Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Shunqin Wang ◽  
Chunyuan Deng
Keyword(s):  
Group Inverse ◽  
Linear Combinations ◽  
Idempotent Operators ◽  
Group Inverses

We present some inverses and group inverses results for linear combinations of two idempotents and their products.

A note on the group inverses of block matrices over rings

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3685-3692
Author(s):  
Hanyu Zhang
Keyword(s):  
Associative Ring ◽  
Sufficient Conditions ◽  
Block Matrix ◽  
Necessary And Sufficient Conditions ◽  
Group Inverse ◽  
Block Matrices ◽  
Group Inverses ◽  
Necessary And Sufficient

Suppose R is an associative ring with identity 1. The purpose of this paper is to give some necessary and sufficient conditions for the existence and the representations of the group inverse of the block matrix (AX+YB B A 0) and M = (A B C D) under some conditions. Some examples are given to illustrate our results.

scholarly journals A weak group inverse for rectangular matrices

2019 ◽  
Vol 113 (4) ◽  
pp. 3727-3740 ◽  
Author(s):  
D. E. Ferreyra ◽  
V. Orquera ◽  
N. Thome
Keyword(s):  
Group Inverse ◽  
Weak Group

Weak group inverses and partial isometries in proper *-rings

2021 ◽  
pp. 1-16
Author(s):  
Mengmeng Zhou ◽  
Jianlong Chen ◽  
Yukun Zhou ◽  
Néstor Thome
Keyword(s):  
Partial Isometries ◽  
Weak Group ◽  
Group Inverses

On Group Inverses of Matrices with Order and Rank Perturbations

1994 ◽  
Vol 44 (3-4) ◽  
pp. 209-222 ◽  
Author(s):  
P.S.S.N.V.P. Rao
Keyword(s):  
Markov Chains ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Group Inverse ◽  
Necessary And Sufficient Condition ◽  
Matrix Formula ◽  
Group Inverses ◽  
Finite Markov Chains ◽  
Necessary And Sufficient

Group inverse of a square matrix A exists if and only if rank of A is equal to rank of A2. Group inverses have many applications, prominent among them is in the analysis of finite Markov chains discussed by Meyer (1982). In this note necessary and sufficient conditions for the existence of group inverses of bordered matrix, [Formula: see text] are obtained and expressions for the group inverses in terms of group inverse of A are given, whenever they exist. Also necessary and sufficient condition for the existence of group inverse of A in terms of group inverse of B and C are given. An application to perturbation in Markov chains is illustrated.

scholarly journals Further characterizations of the weak group inverse of matrices and the weak group matrix

2021 ◽  
Vol 6 (9) ◽  
pp. 9322-9341
Author(s):  
Hui Yan ◽  
◽  
Hongxing Wang ◽  
Kezheng Zuo ◽  
Yang Chen ◽  
...  
Keyword(s):  
Group Inverse ◽  
Weak Group ◽  
Group Matrix
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