Three limit representations of the core-EP inverse

Zhou, Mengmeng; Chen, Jianlong; Li, Tingting; Wang, Dingguo

doi:10.2298/fil1817887z

Cited by 49 publications

(14 citation statements)

References 12 publications

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“…, then the left core-EP inverse A ○ † of A ∈ C n×n is similar to the * core inverse introduced in [4], and the dual core-EP inverse introduced in [42]. According to [4], we have the following representations the core-EP inverses of A ∈ C n×n :…”

Section: Definitionmentioning

confidence: 99%

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Determinantal Representations of the Core Inverse and Its Generalizations with Applications

Kyrchei

2019

Journal of Mathematics

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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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Section: Definitionmentioning

confidence: 99%

“…anks to [42], the following representations of the core-EP inverses will be used for their determinantal representations.…”

Section: Definitionmentioning

confidence: 99%

Determinantal Representations of the Core Inverse and Its Generalizations with Applications

Kyrchei

2019

Journal of Mathematics

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“…Thanks to [36], the following representations of the core EP inverses will be used for their determinantal representations.…”

Section: Determinantal Representations Of the Core Ep Inversesmentioning

confidence: 99%

Determinantal Representations of the Quaternion Core Inverse and Its Generalizations

Kyrchei

2019

Adv. Appl. Clifford Algebras

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In this paper we extend notions of the core inverse, core EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field H and get their determinantal representations within the framework of the theory of column-row determinants previously introduced by the author. Since the Moore-Penrose inverse and the Drazin inverse are necessary tools to represent these generalized inverses, we use their determinantal representations previously obtained by using row-column determinants. As the special case, we give their determinantal representations for matrices with complex entries as well. A numerical example to illustrate the main result is given.

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“…Prasad, Raj, and Vinay in [25] introduced an iterative method to approximate the core-EP inverse. Three limit representations of the core-EP inverse were proposed in [33]. The notion of the core inverse was generalized to the core-EP inverse.…”

Section: Introduction Background and Motivationmentioning

confidence: 99%