Reading again this discusion i have noticed that eigenspaces behaviour is not what i expected:
sage: M=matrix(QQ,[[1,2],[3,4]]) sage: M.eigenspaces() [ (a0, Vector space of degree 2 and dimension 1 over Number Field in a0 with defining polynomial x^2 - 5*x - 2 User basis matrix: [ 1 1/3*a0 - 1/3]) ] sage: M.eigenvalues() [-0.3722813232690144?, 5.372281323269015?] sage: M.eigenvectors_left() [(-0.3722813232690144?, [(1, -0.4574271077563382?)], 1), (5.372281323269015?, [(1, 1.457427107756339?)], 1)] It shows just one of the two eigenspaces (which are Galois conjugate), but that notion deppends on what we consider to be the fase field. This goes against the idea that Rob Beezer pointed (and that sage seems to follow in this context) of considering matrices in a small field to be just a particular case of matrices in bigger fields. Is this the expected behaviour? Miguel -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
