i have trouble in collecting the eigenvectors to form an eigenvector
matrix (in the order given by the eigenvalue computation...).
How can i do this ?
I have tried all matrix commands.
THX.
On Mar 4, 6:22 pm, Jason Grout <jason-s...@creativetrax.com> wrote:
> Alexander Hupfer wrote:
> > thank you for your quick reply.
>
> > Just for sake of documentation:
>
> > the output reads as [[[eigenvalue1, eigenvalue2],[multiplicity of
> > EVal1, multiplicity of EVal2]], Eigenvect of EVal1,..., Eigenvect
> > EVal1, Eigenvect of EVal2,..., Eigenvect of EVal2]
>
> Interestingly, there doesn't seem to be an easy way to tell (from the
> output) which eigenvector goes with which eigenvalue in the following
> examples:
>
> sage: M = matrix(SR,4,4, [[0,1,0,0],[0,0,0,0],[0,0,2,0],[0,0,0,2]]); M
>
> [0 1 0 0]
> [0 0 0 0]
> [0 0 2 0]
> [0 0 0 2]
> sage: M._maxima_().eigenvectors().sage()
> [[[0, 2], [2, 2]], [1, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
> sage: M = matrix(SR,4,4, [[0,0,0,0],[0,0,0,0],[0,0,2,1],[0,0,0,2]]); M
>
> [0 0 0 0]
> [0 0 0 0]
> [0 0 2 1]
> [0 0 0 2]
> sage: M._maxima_().eigenvectors().sage()
> [[[0, 2], [2, 2]], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0]]
>
> I believe MMA helps you by making sure that the list ofeigenvectorsis
> exactly as long as the sum of the multiplicities by inserting zero
> vectors where needed (in other words, you can just count multiplicities
> to get a generating set for the eigenspace). The Sage
> eigenvectors_right command avoids the problem by returning a set
> ofeigenvectorsassociated with each eigenvalue.
>
> Thanks,
>
> Jason
>
>
>
> > On 4 Mrz., 12:44, Jason Grout <jason-s...@creativetrax.com> wrote:
> >> sonium wrote:
> >>> Hi, I have problems calculating theeigenvectorsof asymbolicmatrix.
> >>> I tried:
> >>> a,b = var('a'),var('b')
> >>> M = matrix(SR,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
> >>> M.eigenvectors_right()
> >>> what results in:
> >>> AttributeError: 'SymbolicArithmetic' object has no attribute 'degree'
> >> This comes from us not having a special implementation of the eigen
> >> functions forsymbolicmatrices (i.e., using maxima). For now, you can do:
>
> >> sage: a,b = var('a'),var('b')
> >> sage: M = matrix(SR,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
> >> sage: M._maxima_().eigenvectors().sage()
> >> [[[-a, a], [2, 2]], [0, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 0]]
>
> >> Seehttp://maxima.sourceforge.net/docs/manual/en/maxima_25.html#Item_003a...
> >> to understand the output of the command.
>
> >> The specific error you received came from there not being a .degree()
> >> method for asymbolicpolynomial.
>
> >>> and
> >>> P.<a,b> = PolynomialRing(QQ)
> >>> M = matrix(P,4,4,((a, 0, 0, 0), (0,-a,0,0), (0,0,a,0), (0,0,0,-a)))
> >>> M.eigenvectros_right()
> >>> what gives:
> >>> Traceback (most recent call last):
> >>> File "<stdin>", line 1, in <module>
> >>> File "/home/sage/sagenb/sage_notebook/worksheets/sonium/1/code/
> >>> 26.py", line 6, in <module>
> >>> M.eigenvectors_right()
> >>> File "/home/sage/sage_install/sage-a/local/lib/python2.5/site-
> >>> packages/SQLAlchemy-0.4.6-py2.5.egg/", line 1, in <module>
> >>> File "matrix2.pyx", line 3054, in
> >>> sage.matrix.matrix2.Matrix.eigenvectors_right (sage/matrix/matrix2.c:
> >>> 18020)
> >>> File "matrix2.pyx", line 3000, in
> >>> sage.matrix.matrix2.Matrix.eigenvectors_left (sage/matrix/matrix2.c:
> >>> 17523)
> >>> File "matrix2.pyx", line 2755, in
> >>> sage.matrix.matrix2.Matrix.eigenspaces_left (sage/matrix/matrix2.c:
> >>> 16250)
> >>> File "matrix2.pyx", line 1058, in sage.matrix.matrix2.Matrix.fcp
> >>> (sage/matrix/matrix2.c:7456)
> >>> File "polynomial_element.pyx", line 2288, in
> >>> sage.rings.polynomial.polynomial_element.Polynomial.factor (sage/rings/
> >>> polynomial/polynomial_element.c:18681)
> >>> NotImplementedError
> >> I'm not sure what is going on here...
>
> >> Thanks,
>
> >> Jason
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to
sage-support-unsubscr...@googlegroups.com
For more options, visit this group at
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
