# How does one detect cyclic vectors in SAGE?

Given a vector $v$ and a matrix $A$ of dimension $n$, one would say that $v$ is a cyclic vector of $A$ if the following set is linearly independent ${ v,Av,A^2v,..,A^{n-1}v }$.

Is there a way to test this property on SAGE given a $v$ and a $A$?