Eigenvectors of matrices over finite fields

asked 2018-11-22 18:17:02 +0200

Ramachandran gravatar image

updated 2018-11-22 18:17:30 +0200

Hi. Is there a command which computes the eigenvectors of matrices over finite fields (if it exists). The eigenvalue command does compute the eigenvalues of the matrix but the eigenvectors_right() gives an error. Is there a workaround for this problem.

Thanks in advance.

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Please add an example and the error you get.

rburing gravatar imagerburing ( 2018-11-22 20:55:38 +0200 )edit

@Ramachandran You probably need to at least be working over a splitting field of the characteristic polynomial of your matrix:

L = charpoly.splitting_field('a')
eigenvectors_L = matrix(L,U).eigenvectors_right()

Otherwise you might get an error:

NotImplementedError: eigenvectors are not implemented for matrices with eigenvalues that are not in the fraction field of the base ring or in QQbar

HTH

jwalters gravatar imagejwalters ( 2025-03-06 09:27:07 +0200 )edit
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