Eigensystem applied to a unitary matrix crashes Mathematica 4.
- To: mathgroup at smc.vnet.net
- Subject: [mg21057] Eigensystem applied to a unitary matrix crashes Mathematica 4.
- From: "Ingolf Dahl" <f9aid at fy.chalmers.se>
- Date: Sun, 12 Dec 1999 23:51:22 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
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