Compositions and decompositions of binary relations
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2022
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Mark
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Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky
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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 ◦ 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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Mathematics for Applications. 2022 vol. 11, č. 2, s. 107-117. ISSN 1805-3629
http://ma.fme.vutbr.cz/archiv/11_2/ma_11_2_chajda_langer_final.pdf
http://ma.fme.vutbr.cz/archiv/11_2/ma_11_2_chajda_langer_final.pdf
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en
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© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky