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