Revisiting the core EP inverse and its extension to rectangular matrices

Ferreyra, D. E.; Levis, Fabián Eduardo; Thome, Néstor

doi:10.2989/16073606.2017.1377779

Cited by 108 publications

(55 citation statements)

References 12 publications

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“…(a) Taking into account the expressions (14), (12), and (13) for the determinantal representations of A d , Q A , and P A , respectively, we have…”

Section: Theoremmentioning

confidence: 99%

“…Other generalizations of the core inverse were recently introduced for n × n complex matrices, namely, BT inverses [5], DMP inverses [6], CMP inverses [7], etc. e characterizations, computing methods, some applications of the core inverse, and its generalizations were recently investigated in complex matrices and rings (see, e.g., [3,[8][9][10][11][12][13][14][15][16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…(a) Taking into account the expressions (14), (12), and (13) for the determinantal representations of A d , Q A , and P A , respectively, we have…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Determinantal Representations of the Core Inverse and Its Generalizations with Applications

Kyrchei

2019

Journal of Mathematics

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“…In [24] , the author obtained the relationship between core-EP inverse and core inverse by using the core-EP decomposition. In [12] , some representations for core-EP inverse have been given.…”

Section: Lemma 14 [24]mentioning

confidence: 99%

“…In this section, we mainly show several characterizations of core-EP inverse by applying some properties in [12]. Ferreyra, Levis, et.…”

Section: Some Properties Of Core-ep Inverse Under the Condition Ax = mentioning

confidence: 99%

The new revisitation of core EP inverse of matrices

Zheng

Jie

2019

Filomat

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In this paper, we study some properties of core-EP inverse of square matrices. Firstly, we extend the obtained theorem proved by K.M. Prasad and K.S. Mohana. Then some properties of core-EP inverse have been given, through applying the conditions (AX) * = AX, XA k+1 = A k and R(X) = R(X *) = R(A k). Secondly, we get some characterizations of core-EP inverse by employing the conditions AX = P A k and XA = P R(A k),N((A k+1) * A). Finally, we get some properties of core-EP inverse by utilizing the condition A k+1 X = A k P A k. (i) XAX = X, (ii) XA = AX, (iii) XA k+1 = A k , for some positive integer k, 2010 Mathematics Subject Classification. 15A09 Keywords. core-EP inverse, core-EP decomposition of matrices, core inverse, the orthogonal projection of matrices.

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“…Recently, an extension of the core-EP inverse from a square matrix to a rectangular matrix was made by Ferreyra et al [11]. Let A ∈ C m×n , W ∈ C n×m and k =max{ind(AW ), ind(W A)}.…”

Section: Introductionmentioning

confidence: 99%

Representations and properties of the W-weighted core-EP inverse

Gao

Chen

Patrício

2018

Linear and Multilinear Algebra

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In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank decomposition and QR decomposition. These representations are expressed in terms of various matrix powers as well as matrix product involving the core-EP inverse, Moore-Penrose inverse and usual matrix inverse. Finally, those representations involving only Moore-Penrose inverse are compared and analyzed via computational complexity and numerical examples.

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Revisiting the core EP inverse and its extension to rectangular matrices

Cited by 108 publications

References 12 publications

Determinantal Representations of the Core Inverse and Its Generalizations with Applications

Determinantal Representations of the Core Inverse and Its Generalizations with Applications

The new revisitation of core EP inverse of matrices

Representations and properties of the W-weighted core-EP inverse

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