[gmx-users] Essential dynamics - concepts

[Tsjerk Wassenaar]

Hi Kavya,

> Thanks sir. I will go through them. However I have referred -
> "A Tutorial on Principle component Analysis" by  Lindsay I Smith.
> Which gave a good understanding about the concepts. Still I
> have some doubts regarding eigen values, as you have told
> I will think over them again.

I know that one :) I'd advise others thinking of using PCA in MD to
also read it...  It also pays off to read a few more, though, to get
slightly different viewing angles and to get used to different ways of
telling the same story.

> But one statement I was not clear from your previous mail  that -
> "An eigenvalue is an RMSF of the collective motion."

I shouldn't have said RMSF, as it's not the root. The first eigenvalue
is the variance or mean square fluctuation of the projection of your
data onto the first eigenvector.

>
> These eigenvalues are the solutions for an Nth order equation
> arising from N X N covar (sorry for using this term again) matrix
> (considering only x component). If we consider this covar matrix
> as a transformation matrix, eigen value would give the magnitude
> and direction by which the eigenvector is transformed linearly.
> Is it correct?

No, the matrix of eigenvectors is a transformation (rotation) matrix.
The eigenvectors in a sense give the directions of motion, and the
eigenvalues the magnitudes.

Cheers,

Tsjerk

-- 
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
* Groningen Institute for Biomolecular Research and Biotechnology
* Zernike Institute for Advanced Materials
University of Groningen
The Netherlands