I am wondering if we have a A= n*p matrix of samples and we run a PC decomposition on it. Say the eigenvector matrix is E, so the samples in the eigenvector space should be B= A*(E)^-1So, I am wondering if there is any rule that the columns of B to be correlated? That is, the first PC loadings and the second PC loadings to be correlated? Thanks! 
Could principle component decomposed coordinates value be correlated to each other?
correlation;dimensionality reduction;pca