Possible bug in Eigenvalues[ ] ???
- To: mathgroup at smc.vnet.net
- Subject: [mg100469] Possible bug in Eigenvalues[ ] ???
- From: Lorents <lorents at amp.te>
- Date: Fri, 5 Jun 2009 03:00:47 -0400 (EDT)
Hello,
I'm using Mathematica v.6.0.1.0 under Windows.
I was using the Eigenvalues function to find the eigenvalues of some
complex matrices when I found a very strange behaviour.
Cutting the problem down to the bone, consider the 2x2 matrices
mat = {{11/3, -(1/3)}, {-(1/3), -7}}
pert={{-1 + \[ImaginaryI], 1/2 + \[ImaginaryI]/2}, {-1, 0}}
I'm interested in the trajectories on the complex plane of the
eigenvalues of A(lambda)= mat + lambda*pert as a function of the
"strength" lambda. I calculated these trajectories in two ways and I get
different results (one of which is the correct one).
--> 1st way
expr = Eigenvalues[mat + \[Lambda] pert];
traj1 = Table[expr, {\[Lambda], 0, 10, 0.1}];
--> 2nd way
traj2 = Table[Eigenvalues[mat + \[Lambda] pert], {\[Lambda], 0, 10, 0.1}];
The resulting lists traj1 and traj2 are NOT the same!
A small notebook showing this problem can be found here:
http://www.homepages.ucl.ac.uk/~ucapllo/test.eig.nb
Any thoughts? Is this behaviour normal?
Lorenzo