My question is may be strange but I wanna lie it any way. The direction of an eigenvector is the most important as we normalize it. This view is right but what about the value of this eigenvector in the high dimensional. May be the idea I want to clear is still not so clear. Suppose I have some face images and I follow the Principal Component Analysis steps to compute the eigenvectors on covariance matrix.
http://en.wikipedia.org/wiki/Eigenface http://www.cse.unr.edu/~zehang/research/gender/methodology.html
The first eigenvector(eigenface you can see it in the figures shown in the above two links) has a pattern which is very close to the face image. In his case, the values of the first eigenvector have some meaning, is it right? and what these values represent?