Revisitation of the core inverse

2015 ◽  
Vol 20 (5) ◽  
pp. 381-385 ◽  
Author(s):  
Gaojun Luo ◽  
Kezheng Zuo ◽  
Liang Zhou
Keyword(s):  
The Core ◽  
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 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.

The Core Inverse of a Product and $$2\times 2$$2×2 Matrices

2017 ◽  
Vol 42 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Yuanyuan Ke ◽  
Long Wang ◽  
Jianlong Chen
Keyword(s):  
The Core ◽  
Core Inverse

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 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.

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