scipy.linalg.eig return complex eigenvalues for covariance matrix?

Question

The eigenvalues of a covariance matrix should be real and non-negative because covariance matrices are symmetric and semi positive definite.

However, take a look at

Answer 1

What you are experiencing is numerical instability due to limitations on floating point precision.

Note that:

(1) MATLAB also returned negative values, but the printing format is set to short and you don't see the full precision of the double stored in memory. Use format long g for printing more decimals

(2) All imaginary parts returned by numpy's linalg.eig are close to the machine precision. Thus you should consider them zero.