# JAMC

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

# Row-column Space Lattices of Some Special Boolean Matrices

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Wu Wan*, Congwen Luo

College of Science, China Three Gorges University, Yichang, Hubei, China.

*Corresponding author: Wu Wan

Published: May 6,2023

## Abstract

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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## How to cite this paper

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 Computation7(1), 167-176.

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