The core inverses of linear combinations of two core invertible matrices

Zhou, Mengmeng; Chen, Jianlong; Wang, Dingguo

doi:10.1080/03081087.2019.1615859

Cited by 9 publications

(3 citation statements)

References 25 publications

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“…Te paper [10] attracted a lot of scholars' attention. Many properties, characterizations, representations, perturbation, and partial ordering of core inverse were presented in [11][12][13][14][15][16]. Many scholars studied the theories of core inverse in rings, C * -algebra and Banach space operator, which can be found in [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse

Sheng

2023

Journal of Mathematics

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In this paper, the algebraic perturbation theorems of the core inverse A # and core-EP inverse A † are discussed for a square singular matrix A with different indices, and the expressions of the algebraic perturbation for these two new generalized inverses are presented. As their applications, some properties of the core inverse A # and core-EP inverse A † are proven again by using the expressions of their algebraic perturbation. In the last section, two numerical examples are considered to demonstrate the main results.

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Section: Introductionmentioning

confidence: 99%

Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse

Sheng

2023

Journal of Mathematics

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“…Core inverses, introduced in [1,2], have been frequently investigated over the past few years [31,32]. Indeed, right weak generalized inverse proposed earlier in [3,8], which was renamed as the core inverse.…”

Section: Introductionmentioning

confidence: 99%

Further results on weighted core inverse in a ring

Das¹,

Sahoo²,

Behera³

2022

Linear and Multilinear Algebra

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The notion of the weighted core inverse in a ring with involution was introduced, recently [ Mosić et al. Comm. Algebra, 2018; 46(6); 2332-2345. In this paper, we explore new representation and characterization of the weighted core inverse of sum and difference of two weighted core invertible elements in ring with involution under different conditions. Further, we discuss reverse order laws and mixed-type reverse order laws for the weighted core invertible elements in a ring.

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“…However, the right weak generalized inverse was proposed [3,4] earlier, which renamed as core inverse. In the literature, many authors have been discussed the core inverse [32,7,29,12], and achieved much in the aspect of representations of other generalized inverses [10,18,30]. Prasad and Mohana [13] discussed Core EP inverse of a square matrix of arbitrary index.…”

Section: Introductionmentioning

confidence: 99%

Characterization and Representation of Weighted Core Inverse of Matrices

Behera¹,

Sahoo²,

Mohapatra³

2020

Preprint

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In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Then, we study some properties of the one sided core and dual core inverse of matrices along with group inverse and weighted Moore-Penrose inverse. Further, by applying the new representation and properties of weighted core inverse of matrix, we discuss a few new results related to the reverse order law for these inverses.

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The core inverses of linear combinations of two core invertible matrices

Cited by 9 publications

References 25 publications

Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse

Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse

Further results on weighted core inverse in a ring

Characterization and Representation of Weighted Core Inverse of Matrices

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The core inverses of linear combinations of two core invertible matrices

Cited by 9 publications

References 25 publications

Algebraic Perturbation Theorems of Core Inverse A ㊮ and Core-EP Inverse

Algebraic Perturbation Theorems of Core Inverse A ㊮ and Core-EP Inverse

Further results on weighted core inverse in a ring

Characterization and Representation of Weighted Core Inverse of Matrices

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Product

Resources

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Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse

Algebraic Perturbation Theorems of Core Inverse $A^{㊮}$ and Core-EP Inverse