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 - http://www.scopus.com/inward/record.url?scp=105000333131&partnerID=8YFLogxK
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 -