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I'm teaching PCA to myself for some environmental data analysis. I understand the intuitive and geometric definition, but I'm not quite sure what exactly it's telling me. What exactly do the eigenvectors say about variance (and of which numbers)? What exactly should I be looking for if I'm interested in the variables most closely related? My intuition is telling me to find the smallest Eigenvector and then look at the eigenvalues in that row to find values with an absolute value greater than .5. Cheers!

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PCA is just a change in the representation base (i.e. vectors used to represent your data). By checking the eigenvalues you can have an idea about the importance of each original vector on building the new representation base. This means that some "features" in the original representation are more important that others for data discrimination.

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