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I did PCA on my data and projected the data on first two eigen vectors. After projection I see that the scatter plot of the data starts from [-1,-1]. My data is all positive. Is it correct for the data to be negative in the projected space.

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Yes, it is, there is no reason why a component cannot have negative values.

Let's take this matrix:

[[1, 1],[0.5, 1]]

The eigenvectors have negative values:

[[ 0.81649658, -0.81649658],
    [ 0.57735027,  0.57735027]]
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