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Hello @tomleung1996,
The step to fix the sign is there because an eigenvector is not just one vector, but all nonzero scalar multiples of that vector. Due to the numerical optimization methods used to calculate the vectors, the sign might flip. Particularly, numpy will return the vector with magnitude 1. Thus, we correct the sign by the correlation with diversity (ubiquity), as more diverse economies (less ubiquitous products) tend to be more complex.
Here is a video by 3Blue1Brown I like about eigenvectors where you can get a better understanding of why the multiples of eigenvectors can be treated the same.
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