The 2 covariance matrices only differ by values at top-right and bottom-left. However, sign of principal component eigen vectors (right column) has flipped.

import numpy as np


cov = np.array([[9369, 7060,   16469],
               [7060,  8127,   23034],
               [16469, 23034,  126402]])

eigenvalues, eigenvectors = np.linalg.eigh(cov)

print('Cov 1')
print(eigenvalues)
print(eigenvectors)

cov2 = np.array([[9369, 7060,   *18969*],
               [7060,   8127,   23034],
               [*18969*,  23034,  126402]])

eigenvalues, eigenvectors = np.linalg.eigh(cov2)

print('Cov 2')
print(eigenvalues)
print(eigenvectors)

Results:

Cov 1
[  1188.72951707   9507.3058357  133201.96464723]
[[-0.5549483   0.82002403  0.13997491]
 [ 0.8280924   0.52849364  0.18696912]
 [-0.07934332 -0.21967035  0.97234231]]
Cov 2
[  1390.92828009   8581.02234156 133926.04937835]
[[-0.57175381  0.80502124 -0.15823521]
 [ 0.817929    0.54427789 -0.18642352]
 [-0.06395096 -0.23601353 -0.96964318]]

How can I either prevent this happening, or ‘correct’ in some way so that sign is same – either positive or negative in both cases?