PCA mapping back to original dimensions

1. Jan 19, 2012

doobs

Assume some matrix M with m rows and n columns. Let C(M) denote the covariance matrix computed from M. With principal component analysis, we compute the eigenvectors of C(M) and choose the first k, for example, based on their ordering according to their corresponding eigenvalues. My question is, if e1,e2,...,ek are the eigenvectors that form the principal components, then how can map these back to the original dimensions of M so that I can say that the original dimensions x1,x2,... of M are the ones corresponding to e1,e2,... Is it possible to do this?