# cyclic vector theorem

Let $K$ be a field, $V$ a $K$-vector space of dimension $n$, and $f:V\longrightarrow V$ a linear transformation. Then $f$ has a cyclic vector if and only if every linear transformation $g:V\longrightarrow V$ which commutes with $f$ is a polynomial of $K[X]$ evaluated in $f$.

Title cyclic vector theorem CyclicVectorTheorem 2013-03-22 14:14:16 2013-03-22 14:14:16 gumau (3545) gumau (3545) 5 gumau (3545) Theorem msc 15A04 CyclicSubspace