Question about the last step of computing the eigenface.

I read the article online about computing the eigenface at http://www.scholarpedia.org/article/Eigenfaces and there are 5 steps to do it.

However, I am confusing about the last step, which is

The eigenvalue and eigenvector matrices of C (Convariance matrix) are L (eigenvalues) and U=A*V*L^{−1/2} (eigenvectors). Where U={u_i} is the collection of eigenfaces.

(Here we have face images stored in a matrix A and C = A*A'. And V is the eigenvector of the covariance matrix C.)

According to my understanding, I would use U = AV to get the eigenface.

Anyone got the idea why we need to use U=A*V*L^{−1/2} as the article mentioned above?

Thanks very much.

Aaronne.