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I applied PCA on an $n\times p$ matrix where $n$ means the number of samples and $p$ means the number of variables, and I am using the 1st principal component (PC) as the new representation of the entire dataset. I confirmed that the 1st PC has the highest variance among all PCs, as expected. But I don't know how to interpret the values in the 1st PC, while before applying PCA a negative or positive value had a meaning. I observed that row means of the original data has a $-0.99$ correlation with the 1st PC, meaning that if a sample had a positive value across all variables, then this sample had a highly negative value in the 1st PC, while a consistent negative value across variables in the original data corresponds to a highly positive sample in the 1st PC. This is extremely confusing. How can I interpret that behavior?
I also realized that all loadings for the 1st PC are negative. I think this might be related to what I observe. Any thoughts?