I'm trying to get the eigenvalues and eigenvectors from a square matrix with the following commands:
import numpy as np
A = matrix([[5,2,0],[3,1,-5],[11,4,-4]])
λ, U = np.linalg.eig(A)
print ('Starting matrix:\n', A)
print('\nEigenvalues:\n', λ)
print('\nEigenvectors:\n', U)
The eigenvalues coincide with other softwares, but the eigenvector not. It makes me wonder what I'm doing wrong?
I think you program has not problem, maybe when you compare with other softwares they give a result without normalization.
Such as say in documentation the numpy.linalg.eig function returns
the normalized (unit “length”) eigenvectors.
https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
As in explained here:
https://stackoverflow.com/questions/31487264/numpy-eigenvalues-correct-but-eigenvectors-wrong
The eigenvectors of a matrix can be scaled by any scalar (a number) and still be the same eigenvectors.
I think you program has not problem, maybe when you compare with other softwares they give a result without normalization.
Such as say in documentation the numpy.linalg.eig function returns
the normalized (unit “length”) eigenvectors.
https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
As in explained here:
https://stackoverflow.com/questions/31487264/numpy-eigenvalues-correct-but-eigenvectors-wrong
The eigenvectors of a matrix can be scaled by any scalar (a number) and still be the same eigenvectors.
I am quoting my answer from Falko:
"
The results are different due to multiple reasons:
Considering the first 4 issues the results are actually pretty close. The singularity shouldn't matter, since there is only one zero eigenvalue, thus the corresponding eigenvector is unique (up to sign and length)."
For more visit please:
https://stackoverflow.com/questions/26589448/numpy-seems-to-produce-incorrect-eigenvectors
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