A binary relation \(R\) is irreflexive (or antireflexive), iff for all \(x\) we have \(\neg xRx\).
rel_is_irreflexive(R)rel_is_irreflexive returns
a single logical value.
an object coercible to a 0-1 (logical) square matrix, representing a binary relation on a finite set.
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 to 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()