Eigenvectors of matrices over finite fields
 
  
 
  
 
 
 
 
 
 
    
        
        asked 6 years ago  
 
 Ramachandran gravatar image  
 
 
 
 
    
        
        updated 6 years ago  
 
 
 
 
 
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 (
    
        6 years ago
    )
@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 (
    
        0 years ago
    )
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