Matrix Differentiation for DGGI, WDGGI and GDGI on Dual Real Matrix Ring

Xue Hua; Shuangzhe Liu; Hongxing Wang

doi:10.1007/s40840-025-01852-2

Matrix Differentiation for DGGI, WDGGI and GDGI on Dual Real Matrix Ring

Xue Hua
, Shuangzhe Liu
, Hongxing Wang

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we study the differentiation for three types of group inverses. Firstly, the dual expression of the differentiation of the dual group generalized inverse (DGGI) is given by using the definition of DGGI, and the dual expression of the differentiation of the weak dual group generalized inverse (WDGGI) is given by using the dual core-nilpotent decomposition. Secondly, the compact formulas are applied to give real expressions for the differentiations of the DGGI, WDGGI and group dual generalized inverse (GDGI), respectively. Finally, a block expression for the differentiation of DGGI is included.

Original language	English
Article number	69
Pages (from-to)	1-28
Number of pages	28
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	48
Issue number	3
DOIs	https://doi.org/10.1007/s40840-025-01852-2
Publication status	Published - 2025

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title = "Matrix Differentiation for DGGI, WDGGI and GDGI on Dual Real Matrix Ring",

abstract = "In this paper, we study the differentiation for three types of group inverses. Firstly, the dual expression of the differentiation of the dual group generalized inverse (DGGI) is given by using the definition of DGGI, and the dual expression of the differentiation of the weak dual group generalized inverse (WDGGI) is given by using the dual core-nilpotent decomposition. Secondly, the compact formulas are applied to give real expressions for the differentiations of the DGGI, WDGGI and group dual generalized inverse (GDGI), respectively. Finally, a block expression for the differentiation of DGGI is included.",

keywords = "Differentiation, Dual group generalized inverse, Group dual generalized inverse, Weak dual group generalized inverse",

author = "Xue Hua and Shuangzhe Liu and Hongxing Wang",

note = "Publisher Copyright: {\textcopyright} Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2025.",

year = "2025",

doi = "10.1007/s40840-025-01852-2",

language = "English",

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TY - JOUR

T1 - Matrix Differentiation for DGGI, WDGGI and GDGI on Dual Real Matrix Ring

AU - Hua, Xue

AU - Liu, Shuangzhe

AU - Wang, Hongxing

N1 - Publisher Copyright: © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2025.

PY - 2025

Y1 - 2025

N2 - In this paper, we study the differentiation for three types of group inverses. Firstly, the dual expression of the differentiation of the dual group generalized inverse (DGGI) is given by using the definition of DGGI, and the dual expression of the differentiation of the weak dual group generalized inverse (WDGGI) is given by using the dual core-nilpotent decomposition. Secondly, the compact formulas are applied to give real expressions for the differentiations of the DGGI, WDGGI and group dual generalized inverse (GDGI), respectively. Finally, a block expression for the differentiation of DGGI is included.

AB - In this paper, we study the differentiation for three types of group inverses. Firstly, the dual expression of the differentiation of the dual group generalized inverse (DGGI) is given by using the definition of DGGI, and the dual expression of the differentiation of the weak dual group generalized inverse (WDGGI) is given by using the dual core-nilpotent decomposition. Secondly, the compact formulas are applied to give real expressions for the differentiations of the DGGI, WDGGI and group dual generalized inverse (GDGI), respectively. Finally, a block expression for the differentiation of DGGI is included.

KW - Differentiation

KW - Dual group generalized inverse

KW - Group dual generalized inverse

KW - Weak dual group generalized inverse

UR - https://www.scopus.com/pages/publications/105000333131

U2 - 10.1007/s40840-025-01852-2

DO - 10.1007/s40840-025-01852-2

M3 - Article

AN - SCOPUS:105000333131

SN - 0126-6705

VL - 48

SP - 1

EP - 28

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 3

M1 - 69

ER -

Matrix Differentiation for DGGI, WDGGI and GDGI on Dual Real Matrix Ring

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