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

2021 ◽  
Vol 7 (3) ◽  
pp. 3630-3647
Author(s):  
Zhimei Fu ◽  
◽  
Kezheng Zuo ◽  
Yang Chen
Keyword(s):  
Null Space ◽  
Matrix Equations ◽  
Range Space ◽  
The Core ◽  
Core Inverse ◽  
Core Matrix ◽  
Equivalent Conditions

<abstract><p>The present paper is devoted to characterizing the weak core inverse and the weak core matrix using the core-EP decomposition. Some new characterizations of the weak core inverse are presented by using its range space, null space and matrix equations. Additionally, we give several new representations and properties of the weak core inverse. Finally, we consider several equivalent conditions for a matrix to be a weak core matrix.</p></abstract>

scholarly journals Rank equalities related to a class of outer generalized inverse

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5611-5622 ◽  
Author(s):  
Jianlong Chen ◽  
Sanzhang Xu ◽  
Julio Benítez ◽  
Xiaofeng Chen
Keyword(s):  
Generalized Inverse ◽  
Drazin Inverse ◽  
The Core ◽  
Core Inverse ◽  
Equivalent Conditions

In 2012, Drazin introduced a class of outer generalized inverse in a ring R, the (b,c)-inverse of a for a, b, c ? R and denoted by a||(b,c). In this paper, rank equalities of AkA||(B,C)- A||(B,C)Ak and (A*)kA||(B,C)- A||(B,C)(A*)k are obtained. As applications, weinvestigate equivalent conditions for the equalities (A*)kA||(B,C) = A||(B,C)(A*)k and AkA||(B,C) = A||(B,C)Ak. As corollaries we obtain rank equalities related to the Moore-Penrose inverse, the core inverse, and the Drazin inverse. The paper finishes with some rank equalities involving different e

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.

Further results on the reverse order law for the Core inverse in C*-algebras

2021 ◽  
Vol 67 (8) ◽  
pp. 50-60
Author(s):  
Krishnaswamy D ◽  
Vijayaselvi V
Keyword(s):  
Reverse Order ◽  
C Algebras ◽  
The Core ◽  
Reverse Order Law ◽  
Core Inverse

Regular factorizations and perturbation analysis for the core inverse of linear operators in Hilbert spaces

2018 ◽  
Vol 96 (10) ◽  
pp. 1943-1956 ◽  
Author(s):  
Qianglian Huang ◽  
Saijie Chen ◽  
Zhirong Guo ◽  
Lanping Zhu
Keyword(s):  
Hilbert Spaces ◽  
Perturbation Analysis ◽  
Linear Operators ◽  
The Core ◽  
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.

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 Determinantal Representations of the Core Inverse and Its Generalizations

2020 ◽  
Author(s):  
Ivan I. Kyrchei
Keyword(s):  
The Core ◽  
Core Inverse

scholarly journals A sofic system which is not spectrally of finite type

1988 ◽  
Vol 8 (3) ◽  
pp. 483-490 ◽  
Author(s):  
Susan Williams
Keyword(s):  
Finite Type ◽  
Subshift Of Finite Type ◽  
The Core ◽  
Sofic System ◽  
Core Matrix

AbstractWe exhibit a transitive sofic system for which the core matrix has negative trace, and hence cannot share the nonzero spectrum of any subshift of finite type cover. We also show that every transitive sofic system has an integral core matrix.

Core dimension group constraints for factors of sofic shifts

1993 ◽  
Vol 13 (1) ◽  
pp. 213-224 ◽  
Author(s):  
Paul Trow ◽  
Susan Williams
Keyword(s):  
Characteristic Polynomial ◽  
The Core ◽  
Sofic Shift ◽  
Dimension Group ◽  
Core Matrix ◽  
Sofic Shifts ◽  
Factor Maps

AbstractWe give constraints on the existence of factor maps between sofic shifts. These constraints yield examples of sofic shifts of entropy lognwhich do not factor onto the fulln-shift. We also show that any prime which divides the degree of an endomorphism of a sofic shift must divide the non-leading coefficients of the characteristic polynomial of the core matrix of the shift.

Note on the core matrix partial ordering

2011 ◽  
Vol 31 (1-2) ◽  
pp. 71 ◽  
Author(s):  
Jacek Mielniczuk
Keyword(s):  
Partial Ordering ◽  
The Core ◽  
Core Matrix
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