Re: GramSchmidt problem

• To: mathgroup at smc.vnet.net
• Subject: [mg57044] Re: GramSchmidt problem
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Thu, 12 May 2005 22:44:28 -0400 (EDT)
• Organization: The University of Western Australia
• References: <d5uvda\$9at\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <d5uvda\$9at\$1 at smc.vnet.net>,
Heath Gerhardt <heathgerhardt at hotmail.com> wrote:

> Does anyone know if there are any know problems with GramSchmidt
> crashing Mathematica? When I run it on these 4 25-dimensional vectors it
> crashes on my system:

Tt works perfectly with floating point vectors so I expect that it
crashes because it is not simplifying the intermediate radical
expressions.

Here is functional code for computing GramSchmidt:

GramSchmidt := Fold[Append[#1, FullSimplify[
(#/Norm[#]&)[Fold[Projection, #2, #1]]]] & , {}, #1] & ;

where the projection operator is

Projection[f_, g_] := FullSimplify[f - (f.g) g]

FullSimplify has been used in both routines so that expressions

Calling your set of 4 vectors mat, one computes the orthonormal vectors
using

GramSchmidt[mat]

As a check,

Simplify[% . Transpose[%]]

Cheers,
Paul

--
Paul Abbott                                      Phone: +61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul
http://InternationalMathematicaSymposium.org/IMS2005/

```

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