Eigenline
= Eigenline
An eigenline is a one-dimensional <vector subspace> spanned by an <eigenvector>. If $Av=\lambda v$ with $v\ne0$, then $A(av)=\lambda av$ for every <scalar> $a$, so the line is an <invariant subspace>. It can be contained in an <eigenspace> of larger <dimension>; an eigenline need not be the whole <eigenspace>.