[SciPy-User] qr decompostion gives negative q, r ?

Daπid davidmenhur@gmail....
Tue Nov 20 15:33:30 CST 2012

The QR descomposition is finding two matrices with certain properties such that:

A = Q·R

But, if both Q and R are multiplied by -1, (-Q)·(-R) = Q·R = A, still
the same matrix. If Q is orthogonal, -Q is also. The sign is,
therefore, arbitrary.

On Tue, Nov 20, 2012 at 12:01 AM, Virgil Stokes <vs@it.uu.se> wrote:
> I am using the latest versions of numpy (from
> numpy-1.7.0b2-win32-superpack-python2.7.exe) and scipy (from
> scipy-0.11.0-win32-superpack-python2.7.exe ) on a windows 7 (32-bit)
> platform.
> I have used
> import numpy as np
> q,r = np.linalg.qr(A)
> and compared the results to what I get from MATLAB (R2010B)
> [q,r] = qr(A)
> The q,r returned from numpy are both the negative of the q,r returned
> from MATLAB for the same matrix A. I believe that theq,r returned from
> MATLAB are correct. Why am I getting their negative from numpy?
> Note, I have tried this on several different matrices ---  numpy always
> gives the negative of MATLAB's.
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