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<p>This paper extends the concepts of weighted Drazin-star (WDS) and weighted star-Drazin (WSD) matrices to domain of quaternion matrices. We develop determinantal representations for these matrices, leveraging the theory of noncommutative row-column determinants, considering both general and Hermitian cases. As specific instances, we derive the determinantal representations of the complex WDS and WSD matrices by employing minors of appropriately constructed complex matrices. Furthermore, we investigate two-sided quaternion equations, along with one-sided particular types, where the unique solutions are expressed using WDS and WSD matrices. Explicit solutions for these quaternion matrix equations are obtained using Cramer-type methods. Finally, a numerical example is provided to confirm applicability and efficacy of our findings.</p>

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Restricted Quaternion Two-Sided Matrix Equations with Weighted Drazin-Star and Star-Drazin Solutions

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Ivan I. Kyrchei,
  • Dijana Mosić,
  • Predrag Stanimirović

摘要

This paper extends the concepts of weighted Drazin-star (WDS) and weighted star-Drazin (WSD) matrices to domain of quaternion matrices. We develop determinantal representations for these matrices, leveraging the theory of noncommutative row-column determinants, considering both general and Hermitian cases. As specific instances, we derive the determinantal representations of the complex WDS and WSD matrices by employing minors of appropriately constructed complex matrices. Furthermore, we investigate two-sided quaternion equations, along with one-sided particular types, where the unique solutions are expressed using WDS and WSD matrices. Explicit solutions for these quaternion matrix equations are obtained using Cramer-type methods. Finally, a numerical example is provided to confirm applicability and efficacy of our findings.