Loop of a matroid
= Loop of a matroid
{title2=$r(\{x\})=0$}
= Matroid loop
{synonym}
An element $x$ is a <loop of a matroid> when its <singleton> is not a <matroid independent set>. By heredity, no <matroid independent set> contains it. Equivalently its <singleton> has <rank of a matroid> zero, or it belongs to the <closure of a matroid> of the <empty set>. In a <graphic matroid>, a <self-loop> is a <loop of a matroid>.