Dear all, I diagonalized a given 3x3 matrix, ie found the eigenvalues and eigenvectors, manually. I wanted to check my answer with Sage: M = matrix([[8,-3,-3],[-3,8,-3],[-3,-3,8]]) show(M) O = matrix([[1/sqrt(3),1/sqrt(2),1/sqrt(6)],[1/sqrt(3),-1/sqrt(2),1/ sqrt(6)],[1/sqrt(3),0,-2/sqrt(6)]]) OT = O.transpose() show(O) show(OT) show(OT * O) diag = matrix([[2,0,0],[0,11,0],[0,0,11]]) show(diag) show(O * diag * OT) show(OT * M * O)
M is my given matrix, O is a matrix with the eigenvectors as columns, and OT is the transpose of O. show(OT*O) works as expected, and gives the unit matrix. When I show (OT * M * O), however, the first and third rows are as expected ([2,0,0] and [0,0,11], it the eigenvalues, as in the matrix diag). The second line is a bit wierd though. I get something that should evaluate to [zero,11,zero], but it is not being displayed as such. Instead, there are plenty of square roots in it, and Sage is not simplifying it. I've posted the picture here http://galileon.co.uk/matrix.png. x=OT*M*O x.simplify() show(x) did not help either. version() gives 'Sage Version 3.2.2, Release Date: 2008-12-18', its a binary distribution. uname -a gives: Linux carybdis 2.6.27-11-generic #1 SMP Thu Jan 29 19:24:39 UTC 2009 i686 GNU/Linux UBUNTU 8.10 Any ideas? Thanks :) --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
