From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: Algorithm for QU = (QU)^T ?
Date: 27 Apr 2000 16:52:26 -0400
Newsgroups: sci.math.num-analysis,sci.math
Summary: [missing]

In article <Nu1O4.12092$nb2.253873@vixen.cso.uiuc.edu>,
Jim Ferry  <jferry@[delete_this]uiuc.edu> wrote:
:Does anyone know of an algorithm for the following:
:
:Given an upper triangular matrix U, find an orthogonal matrix Q
:such that QU is symmetric.
:

(U can be any real square matrix, and there seems to be no advantage to
be taken from upper triangularity of U): 
 If singular value decomposition is available then decompose

    U = L * S * R'    (dash means transpose)

with L and R orthogonal and S non-negative diagonal with non-increasing
diagonal entries;

and then the desired Q is Q = R * L'

with the extra feature that Q * U is non-negative semidefinite, and R is
a matrix of its (column) eigenvectors.

In case U is invertible, there is a formula for Q which requires knowing
and inverting the p.d. square root of a p.d. matrix:

  Q = (U' * U)^(-1/2) * U'

Cheers, ZVK(Slavek).