The transformation=True fails even for matrix(QQ,[[0,1,0],[0,0,0], [0,0,0]]). It looks like the algorithm to construct it is flawed, and will not work if there are blocks with the same eigenvalue. Anyone want to re-write this?
-M. Hampton On Oct 12, 9:34 pm, Rob Beezer <[EMAIL PROTECTED]> wrote: > I have a 6x6 matrix with integer entries, whose eigenvalues are also > integers. I wanted the Jordan canonical form, and the associated > matrix to make the similarity transformation. The Jordan form comes > out nicely, but I can't get the transformation matrix. I've included > the error output below - the error seems more severe without setting > base_ring=QQ. I've also include a legitimate transformation matrix I > worked up by hand (with some help from SAGE!). > > Is this expected behavior? Any usage hints or workarounds? Thanks. > > Rob > > m=matrix(QQ, [[2,0,1,1,0,0],[0,2,1,1,0,0],[2,0,1,0,0,1],[2,0,0,1,1,0], > [0,2,1,0,0,1],[0,2,0,1,1,0]]) > m.jordan_form() > > [4|0|0 0|0 0] > [-+-+---+---] > [0|2|0 0|0 0] > [-+-+---+---] > [0|0|0 1|0 0] > [0|0|0 0|0 0] > [-+-+---+---] > [0|0|0 0|0 1] > [0|0|0 0|0 0] > > p=m.jordan_form(base_ring=QQ, transformation=True) > > Traceback (click to the left for traceback) > ... > ValueError: cannot compute the basis of the Jordan block of size 2 > with > eigenvalue 0 > > Traceback (most recent call last): > File "<stdin>", line 1, in <module> > File "/home/rob/.sage/sage_notebook/worksheets/admin/46/code/98.py", > line 6, in <module> > p=m.jordan_form(base_ring=QQ, transformation=True) > File "/opt/sage-3.1.2/local/lib/python2.5/site-packages/ > SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module> > File "matrix2.pyx", line 4125, in > sage.matrix.matrix2.Matrix.jordan_form (sage/matrix/matrix2.c:23429) > ValueError: cannot compute the basis of the Jordan block of size 2 > with eigenvalue 0 > > p=matrix(QQ,[[1,1,0,1,3,1],[1,-1,0,1,3,1],[1,0,1,1,0,1], > [1,0,-1,-3,-6,0],[1,-2,1,0,0,-8],[1,-2,-1,-2,-6,-3]]) > p.inverse()*m*p == m.jordan_form() > > True --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
