Matlab's pca offers coeff and score as results. Coeff represent the eigenvectors of the covariance matrix of the process in question, while score is the representation of the data in the components space. The variance of the scores is equal to the eigenvalues of the covariance matrix.
However, in Karhunen-Loève's expansion methodology, the original process is decomposed in a sum of random variables multiplied by eigenfunctions.
My question is as follows: do the eigenvectors from the PCA and the eigenfunctions of the Karhunen-Loevè's methodology are the same? Same question about the representation of data in the principal component space and the random variables.