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<p>The concept of unitary diagonalization in indefinite inner product spaces is employed to give canonical representations of three matrix partial orders: space, diamond, and plus. A key contribution of this work lies in the results derived for the Euclidean versions of these orders, which emerge as specific cases within the broader theoretical framework. Furthermore, the study examines the interrelationships among the star, diamond, and plus orders, along with their respective powers.</p>

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Canonical representations of space, diamond and plus matrix partial orders in indefinite inner product spaces

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • K. Kamaraj,
  • A. Karpagam,
  • P. Sam Johnson

摘要

The concept of unitary diagonalization in indefinite inner product spaces is employed to give canonical representations of three matrix partial orders: space, diamond, and plus. A key contribution of this work lies in the results derived for the Euclidean versions of these orders, which emerge as specific cases within the broader theoretical framework. Furthermore, the study examines the interrelationships among the star, diamond, and plus orders, along with their respective powers.