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st: RE: matrix decomposition


From   "Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: matrix decomposition
Date   Tue, 10 Aug 2010 08:18:26 -0500

David if V = A*A' where A is the Cholesky decomposition, you can get any other decomposition of V by multiplying A by an arbitrary orthogonal matrix, say P. Thus

(AP)*(AP)' = APP'A' = AIA' = AA' = V


since by definition, PP' = I


Of course, given A, you would have to figure out how construct P to do what you want and still be orthogonal.


Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of D.Ronayne@warwick.ac.uk
Sent: Tuesday, August 10, 2010 5:46 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: matrix decomposition

Dear all,

I want to get Stata to decompose a variance covariance (pos definite)
matrix, say V, into A*A', where A is not triangular as in the cholesky
decomposition (by the command cholesky(V)), but has other linear
restrictions e.g. zeros in different places. Anyone have any tips/examples
of how to program/command this?

Many thanks for any help,
David
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