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 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 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.

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.

scholarly journals EFFECT OF SPANDEX DENIER OF WEFT CORE SPUN YARN ON PROPERTIES OF FINISHED STRETCH WOVEN FABRIC

2020 ◽  
Vol 7 (7) ◽  
pp. 21-32
Author(s):  
Sunny Pannu ◽  
Meenakshi Ahirwar ◽  
Rishi Jamdigni ◽  
B. K. Behera
Keyword(s):  
Research Work ◽  
Woven Fabrics ◽  
Woven Fabric ◽  
The Core ◽  
Spun Yarn ◽  
Spun Yarns ◽  
Recovery Percentage ◽  
Shape Retention ◽  
Dual Core ◽  
Made In

The woven fabrics containing cotton/spandex core spun yarns possesses very vital properties of stretch, recovery and thus shape retention from the view point of wearing comfort and garment appearance. Spandex present in the core of core spun yarn is the most essential performer behind these properties. An attempt is made in this research work to study the influence of changing spandex denier in core spun yarn on the stretch and functional properties of stretch woven fabrics. The sole objective of this study is to find out whether different stretch, shrinkage and physical properties of stretch woven fabrics depend upon changing spandex percentage achieved by means of change in spandex filament denier. It was observed that by increasing denier of spandex in core spun weft yarns the increase in weft shrinkage diminishes. Dual core weft with spandex provides good elongation percentage and recovery percentage. The fabric with higher denier spandex in yarn shows a decreasing total hand values trend for summer and winter. The results depicts that the fabrics have higher THV for winter suiting fabrics as compared to summer suiting thus are more suitable for the winter wear.

The Democratic Design Framework: Motivations and the Dual Core

2021 ◽  
pp. 53-89
Author(s):  
Michael Saward
Keyword(s):  
Design Framework ◽  
The Core ◽  
Minimum Requirements ◽  
Political Principles ◽  
Dual Core ◽  
Critical Idea

This chapter specifies the features at the heart of the new democratic design framework. Focusing on what motivates the framework, it details the notion of ‘democratic sensibility’ and other features of democracy’s normativity, and democracy’s minimum requirements (the ‘democratic minimum’). This is followed by specification of the critical idea of the ‘dual core’, consisting of (a) practices and (b) political principles. These two interacting elements together form the core of the democratic design framework as a whole. Central to the dynamics of the dual core is the enactment of principles through single or multiple institutionalized practices; the discussion treats this feature in some detail, along with the scope and justification of principles.

scholarly journals Determinantal Representations of the Core Inverse and Its Generalizations with Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ivan I. Kyrchei
Keyword(s):  
Direct Method ◽  
Linear Equations ◽  
Close Relation ◽  
Numerical Example ◽  
Determinantal Representation ◽  
The Core ◽  
Core Inverse ◽  
Cramer’S Rule ◽  
The Right

In this paper, we give the direct method to find of the core inverse and its generalizations that is based on their determinantal representations. New determinantal representations of the right and left core inverses, the right and left core-EP inverses, and the DMP, MPD, and CMP inverses are derived by using determinantal representations of the Moore-Penrose and Drazin inverses previously obtained by the author. Since the Bott-Duffin inverse has close relation with the core inverse, we give its determinantal representation and its application in finding solutions of the constrained linear equations that is an analog of Cramer’s rule. A numerical example to illustrate the main result is given.

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