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<p>This paper addresses the consimilarity and right coneigen-problem within the framework of split quaternion algebra. We first introduce a novel real representation for the split quaternion matrix and investigate its fundamental properties. This representation is then utilized to characterize equivalent classes of split quaternions under consimilarity and to solve the right coneigen-problem of split quaternion matrices. Finally, we present a numerical algorithm for calculating right coneigenvalues and their corresponding coneigenvectors, and demonstrate its effectiveness through numerical examples.</p>

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Algebraic methods for the consimilarity and right coneigen-problem over the split quaternion algebra

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Yuqing Zhang,
  • Zhihan Zhou,
  • Zixiang Meng,
  • Musheng Wei,
  • Fengxia Zhang

摘要

This paper addresses the consimilarity and right coneigen-problem within the framework of split quaternion algebra. We first introduce a novel real representation for the split quaternion matrix and investigate its fundamental properties. This representation is then utilized to characterize equivalent classes of split quaternions under consimilarity and to solve the right coneigen-problem of split quaternion matrices. Finally, we present a numerical algorithm for calculating right coneigenvalues and their corresponding coneigenvectors, and demonstrate its effectiveness through numerical examples.