I think the easiest solution is to write a eigenvector and eigenvalue method for matrices which correct the problem (and together return a different result than eigenspaces). I vaguely remember doing that some time ago, but either (a) William didn't like it and dumped it, (b) it may not have survived a linear algebra code rewrite for an accidental reason, (c) my memory is way off.
+++++++++++++++++++++++++++++++++ On 5/10/07, Hamptonio <[EMAIL PROTECTED]> wrote: > I'd just like to second this, since it confused me for a while. As > far as I've seen, this is not pointed out anywhere in the tutorial or > reference manual. In every book I've used, "eigenvector" means the > right-eigenvector. > > -Marshall Hampton > > On Dec 4 2006, 12:39 pm, David Joyner <[EMAIL PROTECTED]> wrote: > > Here is a completely separate issue witheigenspaces, one related to ease > > of use: > > > > sage: MS = MatrixSpace(QQ,2,2) > > sage: A = MS([[0,-16],[-1,0]]) > > sage: A.eigenspaces() > > [ > > (4, [ > > (1, -4) > > ]), > > (-4, [ > > (1, 4) > > ]) > > ] > > sage: Ae = A.eigenspaces() > > sage: v1 = Ae[0][1][0]; v2 = Ae[1][1][0] > > sage: A*v1 == 4*v1 > > False > > sage: v1*A == 4*v1 > > True > > > > At least in the US, Av = lambda*v is the usual definition, > > not vA = lambda*v (which is more common in Europe I think). > > > > Robert Miller wrote: > > > Should this behavior be happening? > > > > > sage: MM = Matrix(GF(2),[[0]]) > > > sage: MM.eigenspaces() > > > > > Traceback (most recent call last): > > > File "<stdin>", line 1, in <module> > > > File "/home/server2/sage_notebook/worksheets/myworksheet/code/60.py", > > > line 4, in <module> > > > MM.eigenspaces() > > > File "/sage-1.5/local/lib/python2.5/", line 1, in <module> > > > > > File "matrix2.pyx", line 1666, in matrix2.Matrix.eigenspaces > > > File "matrix2.pyx", line 966, in matrix2.Matrix.kernel > > > File > > > "/sage-1.5/local/lib/python2.5/site-packages/sage/modules/free_module.py", > > > line 282, in VectorSpace > > > raise TypeError, "K must be a field" > > > TypeError: K must be a field > > --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
