Question about the last step of computing the eigenface.

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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.

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