JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 37-41.doi: 10.6040/j.issn.1671-9352.0.2024.170

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The orthogonality of matrices over three kinds of semirings

CHENG Chonghua, WANG Aifa*,WANG Lili   

  1. School of Mathematical Sciences, Chongqing University of Technology, Chongqing 400054, China
  • Published:2026-04-08

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Abstract: For n×n matrices A and B, they are considered orthogonal when both AB and BA are zero matrices, and A is deemed self-orthogonal when A2 is a zero matrix. The orthogonality of a specific class of tropical(0,-1)matrices, as well as the self-orthogonality of matrices on binary Boolean algebras and chain semirings is studied. The self-orthogonality of matrices on binary Boolean algebras are studied and the zero-square matrix form on those algebras is ndirectly characterized.

Key words: tropical algebra, orthogonality, binary Boolean algebra, chain semiring

CLC Number: 

  • O151
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