I found a very interesting situation. Could anyone tell me why it happened?
For a matrix, I ran two different pieces of code to calculate its covariance matrix. The 2 results look the same. But there is a huge gap between their determinants. This is the code:
X = np.array([[11,5,3,34,8],[25,9,2,6,345],[96,13,8823,8,4],[92,15,153,9,12],[7,14,345,31,10]])
Xbar, mu, std = normalize(X)
S = (1/Xbar.shape[0]) * np.dot(Xbar.T, Xbar)
print('DIY covariance matrix:\n', S)
print('determinant:\n', np.linalg.det(S))
print('\n')
SbyNp = np.cov(Xbar, rowvar=False, bias=True)
print('numpy.linalg covariance matrix:\n', SbyNp)
print('determinant:\n', np.linalg.det(SbyNp))
np.testing.assert_almost_equal(S, SbyNp)
np.testing.assert_almost_equal(np.linalg.det(S), np.linalg.det(SbyNp))
The result of running:
DIY covariance matrix:
[[ 1. 0.57159341 0.62932008 -0.7149413 -0.27222462]
[ 0.57159341 1. 0.26958072 -0.39024794 -0.29147673]
[ 0.62932008 0.26958072 1. -0.38189298 -0.28405386]
[-0.7149413 -0.39024794 -0.38189298 1. -0.4706952 ]
[-0.27222462 -0.29147673 -0.28405386 -0.4706952 1. ]]
determinant:
-1.4290811771081465e-16
numpy.linalg covariance matrix:
[[ 1. 0.57159341 0.62932008 -0.7149413 -0.27222462]
[ 0.57159341 1. 0.26958072 -0.39024794 -0.29147673]
[ 0.62932008 0.26958072 1. -0.38189298 -0.28405386]
[-0.7149413 -0.39024794 -0.38189298 1. -0.4706952 ]
[-0.27222462 -0.29147673 -0.28405386 -0.4706952 1. ]]
determinant:
5.716324708432541e-17
Why these determinants are different? Is there any error in numpy.linalg.det()?
