Matrices over a commutative semiring that are idempotent with respect to the Hadamard product can be identified with binary relations. These relations form an embedded structure within the semi-additive category of (finite) matrices over the semiring. In this paper we investigate this substructure and its relationship with the collection of all matrices. In particular, we are interested under which properties the idempotent matrices form a (distributive) allegory. Furthermore, we study several relational properties and their natural extension to all matrices.

Relations in linear algebra / Killingbeck, D.; Santos Teixeira, M.; Winter, M.. - In: THE JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING. - ISSN 2352-2216. - 91:(2017), pp. 1-16. [10.1016/j.jlamp.2017.05.003]

Relations in linear algebra

Santos Teixeira M.;
2017

Abstract

Matrices over a commutative semiring that are idempotent with respect to the Hadamard product can be identified with binary relations. These relations form an embedded structure within the semi-additive category of (finite) matrices over the semiring. In this paper we investigate this substructure and its relationship with the collection of all matrices. In particular, we are interested under which properties the idempotent matrices form a (distributive) allegory. Furthermore, we study several relational properties and their natural extension to all matrices.
Killingbeck, D.; Santos Teixeira, M.; Winter, M.
Relations in linear algebra / Killingbeck, D.; Santos Teixeira, M.; Winter, M.. - In: THE JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING. - ISSN 2352-2216. - 91:(2017), pp. 1-16. [10.1016/j.jlamp.2017.05.003]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/296604
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