# PCA features intuition : number/decay of eigenvalues

I have a data set, I calculate the correlation matrix and get eigen values for PCA. I want to intuitively understand following features

1. Number of significant eigenvalues. In my dataset, some matrices have only 3 or 4 significant eigenvalues(the value drops from like 140-200 to 1). However some have relatively large number of significant eigenvalues. After 20-50 eigenvalues, the magnitude drops to 1. What is this telling me ?

2. Magnitude of first few eigenvalues. If I take 3-4 largest values and some data subset have large eigen values and some have less, what is this telling me ?

• Reading you question it sounds like you are referring to the scores rather than the eigenvalues. There is one eigenvalue per eigenvector, not multiple. The eigenvalue is the scalar that scales the unit vector eigenvectors to the mean magnitude that they occur in the dataset (see en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors). The scores are the specific value for that eigenvector per sample. If I have interpreted correctly then the current answer is inappropriate. If the sww has interpreted it correctly then you should edit your question to align with the answer. May 16 '18 at 8:31