Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- To: mathgroup at smc.vnet.net
- Subject: [mg21177] Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Fri, 17 Dec 1999 01:23:04 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <831tqg$fmh@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I'm running Mathematica 4.0.1 on a SGI Octane an I can't reproduce your
result.
I can't asl not understand how the second command should change anything
-- you just
assign a near zero matrix to Out[n].
Regards
Jens
Ingolf Dahl wrote:
>
> I have found peculiar behaviour of the Mathematica function "Eigensystem"
> when applied to a three times three unitary matrix, a not too difficult
> numerical problem. A bug report has been sent to Wolfram, where they have
> replicated the problem. I use Mathematica 4.0.0.0 in a Windows98 system, and
> the behaviour has been reproduced on similar computers. Does anyone know a
> simple workaround, which is more reliable than the function Eigensystem?
>
> First, I can crash the Mathematica kernel if I run the three commands below:
>
> (* Command 1 *) unitarymatrix = {{0.9930716088928089`,
> 0.10787324697095696`, -0.046606246351670044`}, {0.10952232338173687`,
> \
> -0.7059175207950679`,
> 0.699775188553875`}, {0.04258685586088479`, -0.7000312967450015`, \
> -0.7128411767605716`}};
>
> (* Command 2 *) Transpose[Inverse[unitarymatrix]] - unitarymatrix;
>
> (* Command 3 *) {ei, vec} = Eigensystem[unitarymatrix]
>
> Secondly, if we remove Command 2, and run Command 3 repeatedly, we get
> different (incorrect) results each time.
>
> (The behaviour does not seem to be unique to this unitary matrix.)
>
> Ingolf Dahl
> f9aid at fy.chalmers.se