Eigendecomposition problem?

*To*: mathgroup at smc.vnet.net*Subject*: [mg126921] Eigendecomposition problem?*From*: Guido <gbellomo at gmail.com>*Date*: Mon, 18 Jun 2012 05:42:02 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi! I'm having some trouble with this. In the code I define two matrices, then calculate its eigenvalues/eigenvectors, and finally I plot the absolute values of the components of the eigenvectors. The results are consistent with (I'm quite sure) the analytical ones but only below "t approx 30". Above this value, (only) the first plot corresponding to one of the vectors shows some strange behaviour. Any idea? Thanks! This is the code: Clear[a, b, w, g, t] \[Rho]t = {{a, b*Exp[-I*w*t - g*t]}, {b\[Conjugate]*Exp[I*w*t - g*t], 1 - a}}; {e1, e2} = Eigenvalues[\[Rho]t]; {v1, v2} = Eigenvectors[\[Rho]t]; a = 0.6`1000; b = 1`1000 + 2`1000*I; w = 1`1000; g = 1`1000; v1n = Normalize[N[v1, 1000]]; v2n = Normalize[N[v2, 1000]]; Abs1 = {Abs[v1n[[1]]], Abs[v1n[[2]]]}; Abs2 = {Abs[v2n[[1]]], Abs[v2n[[2]]]}; Plot[Abs1, {t, 0, 50}, Filling -> Bottom] Plot[Abs2, {t, 0, 50}, Filling -> Bottom]