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 S1/2 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:
Weirdly Polar - [image: AllF.jpg] This is a neat little structure, and it's truly a pain to synthesize (12 steps from *myo*-inositol). But it now seems to hold the record...
13 hours ago