scholarly journals Characterizations and Representations of Core and Dual Core Inverses

2017 ◽  
Vol 60 (2) ◽  
pp. 269-282 ◽  
Author(s):  
Jianlong Chen ◽  
Huihui Zhu ◽  
Pedro Patricio ◽  
Yulin Zhang
Keyword(s):  
Regular Element ◽  
Reverse Order ◽  
The Core ◽  
Reverse Order Law ◽  
Core Inverse ◽  
Dual Core

AbstractIn 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, the characterizations and representations of the core and dual core inverses of a regular element are considered.

scholarly journals Reverse Order Law for the Core Inverse in Rings

2018 ◽  
Vol 15 (3) ◽  
Author(s):  
Honglin Zou ◽  
Jianlong Chen ◽  
Pedro Patrício
Keyword(s):  
Reverse Order ◽  
The Core ◽  
Reverse Order Law ◽  
Core Inverse

scholarly journals Reverse-order law for core inverse of tensors

2020 ◽  
Vol 39 (2) ◽  
Author(s):  
Jajati Keshari Sahoo ◽  
Ratikanta Behera
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Core Inverse

scholarly journals Three limit representations of the core-EP inverse

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5887-5894 ◽  
Author(s):  
Mengmeng Zhou ◽  
Jianlong Chen ◽  
Tingting Li ◽  
Dingguo Wang
Keyword(s):  
Explicit Expression ◽  
Full Rank ◽  
The Core ◽  
Core Inverse ◽  
Rank Decomposition ◽  
Dual Core

In this paper, we present three limit representations of the core-EP inverse. The first approach is based on the full-rank decomposition of a given matrix. The second and third approaches, which depend on the explicit expression of the core-EP inverse, are established. The corresponding limit representations of the dual core-EP inverse are also given. In particular, limit representations of the core and dual core inverse are derived.

scholarly journals The core and dual core inverse of a morphism with factorization

2019 ◽  
Vol 18 (05) ◽  
pp. 1950098 ◽  
Author(s):  
Tingting Li ◽  
Jianlong Chen
Keyword(s):  
The Core ◽  
Core Inverse ◽  
Dual Core

Let [Formula: see text] be a category with an involution ∗. Suppose that [Formula: see text] is a morphism and [Formula: see text] is an (epic, monic) factorization of [Formula: see text] through [Formula: see text], then [Formula: see text] is core invertible if and only if [Formula: see text] and [Formula: see text] are both left invertible if and only if [Formula: see text], [Formula: see text] and [Formula: see text] are all essentially unique (epic, monic) factorizations of [Formula: see text] through [Formula: see text]. We also give the corresponding result about dual core inverse. In addition, we give some characterizations about the coexistence of core inverse and dual core inverse of an [Formula: see text]-morphism in the category of [Formula: see text]-modules of a given ring [Formula: see text].

scholarly journals Core and dual core inverses of a sum of morphisms

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2931-2941 ◽  
Author(s):  
Tingting Li ◽  
Jianlong Chen ◽  
Dingguo Wang ◽  
Sanzhang Xu
Keyword(s):  
Jacobson Radical ◽  
The Core ◽  
Unital Ring ◽  
Additive Category ◽  
Core Inverse ◽  
Dual Core

Let C be an additive category with an involution *. Suppose that ? : X ? X is a morphism of C with core inverse ?# : X ? X and ? : X ? X is a morphism of C such that 1X + ?#? is invertible. Let ? = (1X+?#?)-1, ? = (1X+??#)-1, ? = (1X-??#)??(1X-?#?), ? = ?(1X-?#?)?-1??#?,? = ??#??-1(1X-??#)?,? = ?*(?#(*?*(1X-??#)?. Then f = ? + ? ? ? has a core inverse if and only if 1X-?, 1X-? and 1X-? are invertible. Moreover, the expression of the core inverse of f is presented. Let R be a unital *-ring and J(R) its Jacobson radical, if a ? R# with core inverse a # and j ? J(R), then a + j ? R# if and only if (1-aa#)j(1+a#j)-1(1-a#a) = 0. We also give the similar results for the dual core inverse.

The core and dual core inverse of a morphism with kernel

2018 ◽  
Vol 67 (10) ◽  
pp. 1937-1947
Author(s):  
Tingting Li ◽  
Jianlong Chen ◽  
Mengmeng Zhou ◽  
Dingguo Wang
Keyword(s):  
The Core ◽  
Core Inverse ◽  
Dual Core

scholarly journals The core inverse and constrained matrix approximation problem

2020 ◽  
Vol 18 (1) ◽  
pp. 653-661 ◽  
Author(s):  
Hongxing Wang ◽  
Xiaoyan Zhang
Keyword(s):  
Unique Solution ◽  
Approximation Problem ◽  
Frobenius Norm ◽  
Matrix Approximation ◽  
The Core ◽  
Core Inverse

Abstract In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse: ||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in {\mathcal R} (M), where M\in {{\mathbb{C}}}_{n}^{\text{CM}} . We get the unique solution to the problem, provide two Cramer’s rules for the unique solution and establish two new expressions for the core inverse.

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