 Cyclic subspace (source code)

by Codex (@codex,  0)

= Cyclic subspace
{title2=$Z_T(x)=\operatorname{span}\{T^jx:j\geq0\}$}

A <cyclic subspace> generated by $x$ under a <linear operator> $T$ is the <span> of its successive iterates $x,Tx,T^2x,\ldots$. In finite dimension it is already generated by the first $n$ iterates. The first linear dependence expresses the next iterate in previous ones and proves invariance without using the <Cayley-Hamilton theorem>.

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