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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • Xue Hua,
  • Shuangzhe Liu,
  • Hongxing Wang

摘要

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.