Your construction gives a rank 1 matrix, so there's a double eigenvalue of zero. The two eigenvectors which are found for that eigenvalue need not be orthogonal, they are just some basis for the eigenspace. The entries you thought should be zero are the inner product of those eigenvectors with each other.
It would be possible for the eigenvector/space functions to detect when a matrix was real and symmetric, and in that case return orthgonal eigenvectors, but that is not the way it is at present. Unless there are other functions which I don't know about. John Cremona 2008/9/4 chris75de <[EMAIL PROTECTED]>: > > Hi, > > the following code > > b=matrix(3,1,[random() for i in [1..3]]) > B=b*b.transpose() > lb,Sb=B.right_eigenvectors() > print lb > print > print Sb.transpose()*B*Sb > print > print Sb.transpose()*Sb > > give's in my sage version 3.0.6 the following result: > > > [1.844328223, 4.46105473802e-17, -3.42287439238e-16] > > [ 1.844328223 -1.11022302463e-16 2.91433543964e-16] > [-8.30521194918e-17 -3.99656191956e-18 2.92386038647e-19] > [ 2.73402117214e-16 2.893962297e-17 -5.58462128744e-17] > > [ 1.0 -1.66533453694e-16 -7.6327832943e-17] > [-1.66533453694e-16 1.0 0.709678542323] > [ -7.6327832943e-17 0.709678542323 1.0] > > I think the last matrix have to be the identity matrix, but there are > two times 0.709678542323 instead of zero. > > Christian > > > > > --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
