Compositions and decompositions of binary relations

Ivan Chajda; Helmut Länger

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arXiv · 2111.06282

Compositions and decompositions of binary relations

Ivan Chajda·Helmut Länger

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Abstract

It is well-known that to every binary relation on a non-void set I there can be assigned its incidence matrix, also in the case when I is infinite. We show that a certain kind of "multiplication" of such incidence matrices corresponds to the composition of the corresponding relations. Using this fact we investigate the solvability of the equation R o X = S for given binary relations R and S on I and derive an algorithm for solving this equation by using the connections between the corresponding incidence matrices. Moreover, we describe how one can obtain the incidence matrix of a product of binary relations from the incidence matrices of its factors.

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Ivan Chajda, Helmut Länger. 2021-11-11. Compositions and decompositions of binary relations. https://arxiv.org/abs/2111.06282

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