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

```

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