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The Equivalent Standard Forms of a Class of Tropical Matrices and Centralizer Groups

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  • Yanliang Cheng

    (School of Mathematics, Northwest University, Xi’an 710127, China)

Abstract

In this paper, the equivalent standard forms of tropical idempotent strongly definite matrices are introduced. In particular, the observation of the equivalent standard forms of tropical idempotent normal matrices is given. An equivalence relation ρ on the set of all tropical idempotent normal matrices, which is relevant to their centralizer groups, is introduced and studied. It is proved that every ρ -class contains at least one strongly regular tropical idempotent normal matrix. Furthermore, a structural description of the centralizer groups of partial strongly regular tropical idempotent normal matrices is given.

Suggested Citation

  • Yanliang Cheng, 2025. "The Equivalent Standard Forms of a Class of Tropical Matrices and Centralizer Groups," Mathematics, MDPI, vol. 13(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:399-:d:1576948
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    References listed on IDEAS

    as
    1. Lin Yang, 2018. "The Tropical Matrix Groups with Symmetric Idempotents," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, December.
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