# AMBER Archive (2009)Subject: Re: [AMBER] eigenvalues add up to more than trace of matrix

From: Jason Swails (jason.swails_at_gmail.com)
Date: Fri Oct 16 2009 - 08:29:13 CDT

I don't think there's any requirement that each diagonal element be less
than or equal to unity... If that's the case then the trace could certainly
be greater than 1725. Do you have any negative eigenvalues (possibly a
stupid question for a covariance matrix, but in general eigenvalues can be
negative)? Posting the largest eigenvalue does not prove that the sum of
the eigenvalues is not equal to the trace.
Additionally, you can expect some *small* level of fluctuation due to the
way matrices are diagonalized computationally.

All the best,
Jason

On Thu, Oct 15, 2009 at 11:14 PM, Yaw Sing TAN <tanys_at_bii.a-star.edu.sg>wrote:

> Hi,
>
> I have a 1725 by 1725 covariance matrix generated by ptraj. According to
> the output file which contains the calculated eigenvectors and eigenvalues,
> my first eigenvalue of 8571.29110 is higher than 1725. Does this indicate
> an error with ptraj or with my simulation? Here is the ptraj script which I
> used to generate the evecs.dat file:
>
> trajin prod-1n2e_complete.mdcrd
> strip :WAT,Na+
> center :1-585
> image origin center familiar
> matrix covar @CA name cvmat out cvmat.dat
> analyze matrix cvmat out evecs.dat name evecs vecs 20
> analyze modes fluct out rmsfluct.dat stack evecs beg 1 end 5
> analyze modes displ out resdispl.dat stack evecs beg 1 end 5
> go
>
> Thanks for helping!
>
> Yaw Sing
>
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```--
---------------------------------------
Jason M. Swails
Quantum Theory Project,
University of Florida