Thanks!

Is there otherwise any standard operation in SAGE to create such vectors?

If you have time can you also look into another question I had about 
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 $A$?  


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