[R] weird behaviour of eigen()

[Karim Elsawy]

I'm using R 1.7.1 under linux redhat
it seems that the eigen values produced by eigen() do not follow 
a consistant order; I mean either ascending or discending

e.g

for one system:
eigenV<-eigen(V)
>                   print(eigenV$values)
 [1] -7.706828e+13 -4.702980e+13 -3.267579e+13 -1.701297e+13
-8.041677e+12
 [6] -5.707311e+12 -5.053941e+12 -4.774652e+12 -4.280423e+12
-3.798905e+12
[11] -3.422172e+12 -3.148595e+12 -2.974540e+12 -2.881025e+12
-2.730044e+12
[16] -2.476652e+12 -2.216184e+12 -1.996965e+12 -1.852241e+12
-1.419131e+12
[21] -1.307872e+12 -1.248930e+12 -1.244060e+12 -1.092555e+12
-1.069742e+12
[26] -1.064907e+12 -1.007863e+12 -9.894342e+11 -9.459110e+11
-8.017146e+11
[31] -5.619008e+11 -5.443052e+11 -3.834215e+11 -7.530864e+10
-2.820257e+10
[36] -1.757125e+10 -5.503488e+09 -2.225226e+09 -1.106936e+09
-1.035204e-05

> -7.706828e+13 > -1.035204e-05
[1] FALSE

for anther system:
eigenV<-eigen(V)
> print(eigenV$values)
 [1] -8.564110e-03 -1.486071e+08 -8.200752e+08 -2.033989e+09
-3.166960e+09
 [6] -9.511769e+09 -1.067173e+10 -1.207226e+10 -3.779904e+10
-6.752452e+10
[11] -1.717127e+11 -1.781890e+11 -1.887900e+11 -2.566200e+11
-2.908604e+11
[16] -4.027630e+11 -4.813731e+11 -5.072795e+11 -7.635460e+11
-8.442470e+11
[21] -8.938820e+11 -9.533737e+11 -1.038059e+12 -1.155368e+12
-1.297694e+12
[26] -1.502400e+12 -1.577757e+12 -1.748035e+12 -1.948777e+12
-2.234958e+12
[31] -2.586261e+12 -2.635164e+12 -2.705431e+12 -2.714573e+12
-3.189646e+12
[36] -3.313364e+12 -3.405791e+12 -4.951881e+12 -5.396912e+12
-5.681758e+12
[41] -5.964839e+12 -6.782151e+12 -7.234084e+12 -7.328940e+12
-7.421814e+12
[46] -8.129555e+12 -8.226702e+12 -9.268597e+12 -1.003589e+13
-1.076822e+13
[51] -1.136816e+13 -1.456318e+13 -1.903689e+13 -3.804764e+13
-6.641937e+13
[56] -1.547690e+14

> -8.564110e-03 > -1.547690e+14
[1] TRUE

what worries me now is that whether the order of the eigen vectors
follow the
corresponding eigen values or not?????
THIS IS OF PRIME IMPORTANCE.

any help is very much appreciated
best regards
Karim