It seems that this trick does not work for eigenvectors. I would like to know an answer to Shing's question on eigenvectors.
In-Jae ________________________________________ From: [email protected] [[email protected]] On Behalf Of Marshall Hampton [[email protected]] Sent: Monday, September 21, 2009 11:19 AM To: sage-support Subject: [sage-support] Re: Eigenvalues and vectors in radical format If you work over the "symbolic ring" SR (which is not really a formal ring), you get the exact values: sage: M = matrix(SR,[[1,4],[4,2]]) sage: M.eigenvalues() [-1/2*sqrt(65) + 3/2, 1/2*sqrt(65) + 3/2] -M.Hampton On Sep 21, 9:03 am, Shing Hing Man <[email protected]> wrote: > In Sage, the eigenvalues and vectors (over a Rational matrix) returns > the answer in numerical format. > Is it possible to returns the answer in radical format ? > I am aware that I can use the Maxima eigenvectors function in Sage to > get the answer in radical format. It is better if I do need to depend > on Maxima. (Please see example below.) > > sage: sageMatrix = matrix(QQ,[[1,4],[4,2]]) > sage: sageMatrix > [1 4] > [4 2] > sage: sageMatrix.eigenvalues() > [-2.531128874149275?, 5.531128874149275?] > sage: sageMatrix.eigenvectors_right() > [(-2.531128874149275?, [(1, -0.8827822185373187?)], 1), > (5.531128874149275?, [(1, 1.132782218537319?)], 1)] > sage: maximaMatrix=maxima('matrix[[1,4],[2,4]]') > sage: maximaMatrix > matrix[[1,4],[2,4]] > sage: maximaMatrix.eigenvectors() > [[[-(sqrt(41)-5)/2,(sqrt(41)+5)/2],[1,1]],[1,-(sqrt(41)-3)/8],[1,(sqrt > (41)+3)/8]] > > Thanks in advance for any assistance! > > Shing --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
