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 $A$?
You can get the list of vectors as follows:
sage: [A^k*v for k in range(n)]
Then you can check that they are linearly independent by looking at the determinant of the matrix made with those vectors:
sage: det(matrix([A^k*v for k in range(n)]))
Or,
sage: matrix([A^k*v for k in range(n)]).is_invertible()
Asked: 2015-06-04 22:12:06 +0100
Seen: 691 times
Last updated: Jun 05 '15
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