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.;
2017-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
