In sklearn.decomposition.PCA, why are components_ negative?

Question

I\'m trying to follow along with Abdi & Williams - Principal Component Analysis (2010) and build principal components through SVD, using numpy.linalg.svd.

When I

Answer 1

This is a short notice for those who care about the purpose and not the math part at all.

Although the sign is opposite for some of the components, that shouldn't be considered as a problem. In fact what we do care about (at least to my understanding) is the axes' directions. The components, ultimately, are vectors that identify these axes after transforming the input data using pca. Therefore no matter what direction each component is pointing to, the new axes that our data lie on will be the same.