Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- To: mathgroup at smc.vnet.net
- Subject: [mg21236] Re: Eigensystem applied to a unitary matrix crashes Mathematica 4.
- From: "Kevin J. McCann" <kevinmccann at home.com>
- Date: Mon, 20 Dec 1999 02:27:55 -0500 (EST)
- References: <831tqg$fmh@smc.vnet.net> <83cn2s$5o2$8@dragonfly.wolfram.com>
- Sender: owner-wri-mathgroup at wolfram.com
Well it looks like Ingolf has got himself a winner here. I tried it on my
W98 system and Commands 1,2,3 crash the kernel. Further, command 1 followed
by repeated execution of the Eigensystem command gives different results
each time.
Kevin
>
> 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
>
>
>