1 | | In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors. |

| 1 | {{{ |

| 2 | sage: K.<i> = QuadraticField(-1) |

| 3 | sage: L = K.extension(x^2 - 6*x - 4, 'a1') |

| 4 | sage: eigval = L.gen() |

| 5 | sage: eigval_conj = eigval.galois_conjugates(QQbar) |

| 6 | sage: f0 = hom(eigval.parent(), QQbar, eigval_conj[0]) |

| 7 | sage: f1 = hom(eigval.parent(), QQbar, eigval_conj[1]) |

| 8 | sage: f0(i) # wrong embedding!! |

| 9 | 0.?e-54 - 1.000000000000000?*I |

| 10 | sage: f1(i) # wrong embedding!! |

| 11 | 0.?e-54 - 1.000000000000000?*I |

| 12 | }}} |

| 13 | |

| 14 | As the consequence eigenvectors over QQbar could get incorrectly conjugated. In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors. |