Löwdin orthogonalization

Did you know that you can do a Löwdin orthogonalization by a singular value decomposition? Usually, when I hear Löwdin orthogonalization, I think of some weird S^1/2 matrix, which scares me and I tend to stay away from it... But this pdf from the University of Oregon claims that you can do it in a different way. And it seems to work.

Say you have a matrix A and you want an orthogonal matrix that resembles it as closely as possible. What do you do? First you do a singular value decomposition of A:

Here U and V are orthogonal matrices and Λ is a diagonal matrix. We can now construct

which is an orthogonal matrix, since U and V are both orthogonal matrices. But even more, A' is the orthogonal matrix that best resembles A in the sense that for all orthogonal matrices Q it minimizes the distance with respect to the Frobenius norm

That is all you have to do.