Characterization of Rank of a Matrix Over the Symmetrized Max-Plus Algebra

Authors

  • Suroto
  • Diah Junia Eksi Palupi
  • Ari Suparwanto

Keywords:

Characterization, Rank, Linear Independent, Symmetrized Max-Plus Algebra.

Abstract

In this paper, we characterize the rank of a matrix over the symmetrized max-plus algebra. This characterization is based on linearly independence of columns or rows of the matrix in balance sense. We show that the rank of such a matrix can be determined using maximum number of rows or columns which are linearly independent in balance sense. This completes the discussion in [1] which only uses minors to determine rank of matrix.

Key words and phrases. Characterization, Rank, Linear Independent, Symmetrized Max-Plus Algebra.

2010 Mathematics Subject Classification. 15A80, 15A03

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Published

2025-05-18

How to Cite

Suroto, Diah Junia Eksi Palupi, & Ari Suparwanto. (2025). Characterization of Rank of a Matrix Over the Symmetrized Max-Plus Algebra. Jordan Journal of Mathematics and Statistics, 15(4A), 843–856. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/701

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