If I×(S) _ denotes the set of (multiplicative) idempotent elements of a commutative semiring S, then a matrix over S is idempotent with respect to the Hadamard product iff all its coefficients are in I×(S). Since the collection of idempotent matrices can be seen as an embedded structure of binary relations inside the category of matrices over S, we are interested in the relationship between the two structures. In particular, we are interested under which properties the idempotent matrices form a (distributive) allegory.
Relations among matrices over a semiring / Killingbeck, D.; Santos Teixeira, Milene; Winter, M.. - 9348:(2015), pp. 101-118. (Intervento presentato al convegno 15th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2015 tenutosi a Porto nel 2015) [10.1007/978-3-319-24704-5_7].
Relations among matrices over a semiring
Teixeira Santos Milene;
2015-01-01
Abstract
If I×(S) _ denotes the set of (multiplicative) idempotent elements of a commutative semiring S, then a matrix over S is idempotent with respect to the Hadamard product iff all its coefficients are in I×(S). Since the collection of idempotent matrices can be seen as an embedded structure of binary relations inside the category of matrices over S, we are interested in the relationship between the two structures. In particular, we are interested under which properties the idempotent matrices form a (distributive) allegory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
