This notebook contains an excerpt from the Python Programming and Numerical Methods - A Guide for Engineers and Scientists, the content is also available at Berkeley Python Numerical Methods.
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< 15.3 The QR Method | Contents | 15.5 Summary and Problems >
Eigenvalues and Eigenvectors in Python¶
Though the methods we introduced so far look complicated, the actually calculation of the eigenvalues and eigenvectors in Python is fairly easy. The main built-in function in Python to solve the eigenvalue/eigenvector problem for a square array is the eig function in numpy.linalg. Let’s see how we can use it.
TRY IT Calculate the eigenvalues and eigenvectors for matrix \(A = \begin{bmatrix} 0 & 2\\ 2 & 3\\ \end{bmatrix}\).
import numpy as np
from numpy.linalg import eig
a = np.array([[0, 2],
[2, 3]])
w,v=eig(a)
print('E-value:', w)
print('E-vector', v)
E-value: [-1. 4.]
E-vector [[-0.89442719 -0.4472136 ]
[ 0.4472136 -0.89442719]]
TRY IT! Compute the eigenvalues and eigenvectors for matrix \(A = \begin{bmatrix} 2 & 2 & 4\\ 1 & 3 & 5\\ 2 & 3 & 4\\ \end{bmatrix}\).
a = np.array([[2, 2, 4],
[1, 3, 5],
[2, 3, 4]])
w,v=eig(a)
print('E-value:', w)
print('E-vector', v)
E-value: [ 8.80916362 0.92620912 -0.73537273]
E-vector [[-0.52799324 -0.77557092 -0.36272811]
[-0.604391 0.62277013 -0.7103262 ]
[-0.59660259 -0.10318482 0.60321224]]
< 15.3 The QR Method | Contents | 15.5 Summary and Problems >