Work

Transitive Closure Preservers for Matrices over a Class of Semirings

Year: 2026

Type: article

Abstract: We introduce the transitive closure operator Γ on the set of square matrices over a class of semirings, and then define the transitive closure of a matrix. We characterize the surjective linear transformations of matrices preserving (strongly preserving) transitive closures, and show that a surjective linear transformation preserves the transitive closures if and only if it commutes with Γ, which is equivalent to preserving the kernel of Γ. We also deduce that the strong linear preservers of transitive closure on 2×2 matrices over certain inclines are surjective. In particular, we provide a complete characterization of strong linear preservers of transitive closure on n×n matrices over the binary Boolean semiring.

Source: Mathematics

DOI: 10.3390/math14081315

Authors: Weina Deng, Baomin Yu

Institutions: Huanghuai University, Weinan Normal University

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: National Natural Science Foundation of China, Natural Science Foundation of Henan Province