[gmx-users] what do negative eigenvalues imply?

[Chris Neale]

Hello,

I was wondering if anybody can explain why eigenvalues can be negative? 
I have found a suggestion on the internet that this is because the 
positive eigenvalues have accounted for more than 100% of the motion. 
Does this sound accurate?

This system is the alanine dipeptide. I do not find such negative values 
when running g_covar on full proteins.

The contents of eigenval.xvg are listed below.

# This file was created Mon Oct 29 16:31:46 2007
# by the following command:
# /hpf/data/pomes/cneale/exe/gromacs-3.3.1/exec/fftw-3.1.2/bin/g_covar 
-s ../adp.tpr -n ../adp.ndx -f ../adp_0-1.56us.xtc -ascii covar.dat -mwa
#
# /hpf/data/pomes/cneale/exe/gromacs-3.3.1/exec/fftw-3.1.2/bin/g_covar 
is part of G R O M A C S:
#
# Great Red Owns Many ACres of Sand
#
@    title "Eigenvalues of the covariance matrix"
@    xaxis  label "Eigenvector index"
@    yaxis  label "(u nm\S2\N)"
@TYPE xy
         1 0.211327
         2 0.0736961
         3 0.0522046
         4 0.04409
         5 0.0104057
         6 0.00577603
         7 0.00198832
         8 0.00163465
         9 0.00128302
        10 0.000735383
        11 0.000649576
        12 0.000434795
        13 0.000376401
        14 0.000337852
        15 0.000191994
        16 0.000131498
        17 8.87514e-05
        18 7.31975e-05
        19 5.31939e-05
        20 4.45637e-05
        21 -5.03112e-06
        22 -1.26812e-05
        23 -2.48763e-05
        24 -5.90268e-05
        25 -0.000114215
        26 -0.000227912
        27 -0.000355243
        28 -0.000513052
        29 -0.000631471
        30 -0.00178302