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.

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 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 Generalizations of the reverse order law with related results

1974 ◽  
Vol 8 (4) ◽  
pp. 345-349 ◽  
Author(s):  
David T. Barwick ◽  
Jimmie D. Gilbert
Keyword(s):  
Reverse Order ◽  
Reverse Order Law
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