A binary relation \(R\) is irreflexive (or antireflexive), iff for all \(x\) we have \(\neg xRx\).
rel_is_irreflexive(R)
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.
rel_is_irreflexive
returns
a single logical value.
rel_is_irreflexive
finds out if a given binary relation
is irreflexive. The function just checks whether all elements
on the diagonal of R
are zeros,
i.e., it has \(O(n)\) time complexity,
where \(n\) is the number of rows in R
.
Missing values on the diagonal may result in NA
.
When dealing with a graph's loops,
i.e., elements related with themselves, you may be interested
in finding a reflexive closure,
see rel_closure_reflexive
,
or a reflexive reduction,
see rel_reduction_reflexive
.
Other binary_relations: check_comonotonicity
,
pord_nd
, pord_spread
,
pord_weakdom
, rel_graph
,
rel_is_antisymmetric
,
rel_is_asymmetric
,
rel_is_cyclic
,
rel_is_reflexive
,
rel_is_symmetric
,
rel_is_total
,
rel_is_transitive
,
rel_reduction_hasse