[SciPy-User] raising a matrix to float power
Charles R Harris
Sun Jul 11 08:40:00 CDT 2010
On Sun, Jul 11, 2010 at 1:24 AM, Alexey Brazhe <email@example.com> wrote:
> Did I get it right that W(W^TW)^(-1/2)
> reduces to UV, where U,V come from svd of W?
Yep. If W = u * d * v, then (W^TW)^(-1/2) = v^T * 1/d * v and the rest
follows because u and v are orthogonal. The result is an orthogonal matrix
if none of the d's are zeros. This looks like some sort of whitening, so
with some adustments you can probably get equivalent results using the q
from a qr decomposition or even just the u from the svd.
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