= Cyclic vector
{title2=$V=\operatorname{span}\{v,Tv,T^2v,\ldots\}$}
{wiki}
For a <linear operator> $T$, a cyclic vector is a vector whose iterates span the entire <vector space>. In finite <dimension> $d$, the vectors $v,Tv,\ldots,T^{d-1}v$ then form a <basis>: the first linear dependence makes the preceding span invariant under $T$, so later iterates cannot enlarge it. In topological settings one often requires the iterates to have dense span instead; that closure convention must be stated.
Back to article page
