eigenvectors for matrices in AA claim to be not implemented

[sagetrac-tmonteil]

As reported on this ask question, we have:

sage: M=matrix(ZZ,[[0,-1],[1,0]])
sage: M.eigenvectors_right()
[(-1*I, [(1, 1*I)], 1), (1*I, [(1, -1*I)], 1)]

sage: M = M.change_ring(QQbar) 
sage: M.eigenvectors_right()
[(1*I, [
  (1, -1*I)
  ], 1), (-1*I, [
  (1, 1*I)
  ], 1)]

but

sage: M = M.change_ring(AA)
sage: M.eigenvectors_right()
NotImplementedError: eigenvectors are not implemented for matrices with eigenvalues that are not in the fraction field of the base ring or in QQbar

Component: linear algebra

Issue created by migration from https://trac.sagemath.org/ticket/18071