How does one detect cyclic vectors in SAGE?

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asked 9 years ago

Phoenix
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updated 9 years ago

FrédéricC

5426 ●4 ●44 ●121

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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answered 9 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

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()

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Asked: 9 years ago

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Last updated: Jun 05 '15

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