Journal of Applied Mathematics and Computation

DOI：http://dx.doi.org/10.26855/jamc.2023.03.019

Date: May 6,2023 Hits: 179

Firstly, this paper defines a Galois connection between the row and column spaces of Boolean matrices, establishes the basic theorem of the row-column space lattice of Boolean matrices, and proves that any finite lattice is isomorphic to the row-column space lattice of Boolean matrices. Secondly, according to the basic theorem of the row-column space lattice of Boolean matrices, some special Boolean matrices are considered, such as reflexive matrices, symmetric matrices, equivalent matrices, etc. The row-column space lattices of these special Boolean matrices are characterized. It is proved that the row-column space lattice of sym-metric matrix corresponds to Polarity lattice, the row-column space lattice of anti-symmetric matrix corresponds to finite orthogonal lattice, the row-column space lattice of row (column) permutation matrix corresponds to Boolean lattice, etc. Finally, the relationship between row (column) permutation matrix and equivalent matrix is studied.

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**Row-column Space Lattices of Some Special Boolean Matrices**

**How to cite this paper:** Wu Wan, Congwen Luo. (2023) Row-column Space Lattices of Some Special Boolean Matrices. *Journal of Applied Mathematics and Computation*, **7**(**1**), 167-176.

**DOI: http://dx.doi.org/10.26855/jamc.2023.03.019**

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