cyclic vector theorem

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

Title	cyclic vector theorem
Canonical name	CyclicVectorTheorem
Date of creation	2013-03-22 14:14:16
Last modified on	2013-03-22 14:14:16
Owner	gumau (3545)
Last modified by	gumau (3545)
Numerical id	5
Author	gumau (3545)
Entry type	Theorem
Classification	msc 15A04
Related topic	CyclicSubspace