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<p>In this paper, we introduce the notions of the dual DMP inverse and the weak dual DMP inverse for dual matrices. The dual DMP inverse extends the classical DMP inverse to the dual setting, but it is worth noting that it does not always exist. To overcome this deficiency, we propose the weak dual DMP inverse, which is unique and exists for any square dual matrix. By employing the dual core-EP decomposition, we obtain explicit expressions for these two generalized inverses. Furthermore, we investigate their algebraic properties and characterizations, and establish the relationships between them. Finally, we apply the weak dual DMP inverse to obtain the general solutions of a class of restricted dual matrix equations.</p>

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The dual DMP inverse and weak dual DMP inverse: characterizations and applications

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Xiaoji Liu,
  • Mei Luo,
  • Hongxing Wang

摘要

In this paper, we introduce the notions of the dual DMP inverse and the weak dual DMP inverse for dual matrices. The dual DMP inverse extends the classical DMP inverse to the dual setting, but it is worth noting that it does not always exist. To overcome this deficiency, we propose the weak dual DMP inverse, which is unique and exists for any square dual matrix. By employing the dual core-EP decomposition, we obtain explicit expressions for these two generalized inverses. Furthermore, we investigate their algebraic properties and characterizations, and establish the relationships between them. Finally, we apply the weak dual DMP inverse to obtain the general solutions of a class of restricted dual matrix equations.