[Scipy-tickets] [SciPy] #1525: linalg.eig does not normalize eigenvectors

SciPy Trac scipy-tickets@scipy....
Tue Sep 27 10:21:07 CDT 2011

#1525: linalg.eig does not normalize eigenvectors
 Reporter:  blackhorizon                |       Owner:  somebody   
     Type:  defect                      |      Status:  new        
 Priority:  normal                      |   Milestone:  Unscheduled
Component:  scipy.linalg                |     Version:  0.8.0      
 Keywords:  eigenvectors normalization  |  
 scipy.linalg.eig does not seem to normalize the eigenvectors when it is
 solving a generalized eigenvalue problem, while the documentation
 indicates that the vectors should be normalized.

 On an ordinary eigenvalue problem the vectors do seem to be normalized.

 From the documentation : "The normalized right eigenvector corresponding
 to the eigenvalue w[i] is the column vr[:,i]."

 currently experiencing this problem with scipy 0.8.0, under ubuntu linux
 11.04 (natty narwhal)
 I did not test this with other versions.

 code to reproduce the problem :

 import numpy,scipy

 M1 = numpy.random.uniform(size=(100,100))
 M2 = numpy.random.uniform(size=(100,100))

 D,Z = scipy.linalg.eig(M1,M2)

 print numpy.linalg.norm(Z[:,0])

 If the vectors are normalized, the print-statement should print 1.0, but
 instead it produces values that are generally between 3 and 5.

Ticket URL: <http://projects.scipy.org/scipy/ticket/1525>
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