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<p>In this paper, we introduce two new forms of the dual Hartwig–Spindelböck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further explore and characterize the relationships and properties of these inverses, investigate the dual composite generalized inverses, and verify the applicability of dual partial orders. The proposed decomposition provides a convenient tool for the study of dual matrices.</p>

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Further results for the dual Hartwig–Spindelböck decomposition and its applications

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Tan Mei,
  • Kezheng Zuo,
  • Hui Yan

摘要

In this paper, we introduce two new forms of the dual Hartwig–Spindelböck decomposition and employ them to derive explicit representations for several classes of dual generalized inverses. Building on these representations, we further explore and characterize the relationships and properties of these inverses, investigate the dual composite generalized inverses, and verify the applicability of dual partial orders. The proposed decomposition provides a convenient tool for the study of dual matrices.