How to find two largest eigenvector in python?

Question

I can find eigenvectors of a matrix in Python as follows:

from numpy import linalg as LA
w, v = LA.eig(np.diag((1, 2, 3)))

But how to find the largest two eigenvectors for a larger matrix of size 100*200?

A matrix of size 100 x 200 won't have eigenvectors. Did you mean singular values? — ddejohn
– ddejohn, Commented Sep 16, 2021 at 22:03
Does this answer your question? Efficient way to take the minimum/maximum n values and indices from a matrix using NumPy — ddejohn
– ddejohn, Commented Sep 16, 2021 at 22:14

Matt · Accepted Answer · 2021-12-03 20:58:08Z

1

Eigenvalue decomposition is not defined for a non-square matrix. The closest operation is single value decomposition. SVD and EIG for a non-square matrix are related in that the single values are the square root of the eigenvalues of the transpose of the matrix times itself.

B = A' * A
SVD(A) * SVD(A) ~= EIG(B)

So one potential answer to your question is:

import numpy as np
A = np.array([[1,2,3],[4,5,6],[7,8,9],[10,11,12]])
B = np.matmul(np.transpose(A), A)
u,s,v = np.linalg.svd(A)
V, D = np.linalg.eig(B)
print(f'Compare s*s to V {s*s - V}')

While s is not directly the eigenvalues of A it is somewhat related.

edited Dec 3, 2021 at 20:58

answered Sep 17, 2021 at 13:22

Matt

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