In the following: sage: m=matrix(4, range(16)) sage: m.eigenspaces()
[ (0, Vector space of degree 4 and dimension 2 over Rational Field User basis matrix: [ 1 0 -3 2] [ 0 1 -2 1]), (a1, Vector space of degree 4 and dimension 1 over Number Field in a1 with defining polynomial x^2 - 30*x - 80 User basis matrix: [ 1 1/56*a1 + 4/7 1/28*a1 + 1/7 3/56*a1 - 2/7]) ] Apparently the a1 corresponds to two distinct eigenvalues (the roots of that polynomial). Is there an easy way to get the actual, distinct eigenvalues of the matrix from what is returned? Also, where did the two eigenspaces corresponding to those eigenvalues go? I might just need a short tutorial on linear algebra over number fields; I'm not familiar with conventions there. After a bit more poking around, if I do a1.galois_conjugates(RR), I do get the two roots. I presume that if I substitute these into a1 in the above eigenvector, I will get bases for the two eigenspaces? Thanks, Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com 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 -~----------~----~----~----~------~----~------~--~---
