[gmx-users] definition of "eigenvector" in gromacs

[Tsjerk Wassenaar]

Hi Brett,

Let's say you're sitting at your _desk_ writing that paper with a deadline
yesterday and you put a quick _meal_ next to you, wondering why on _earth_
you keep up with this. Your hands are moving between the meal and the
keyboard. You notice that the average position of your hands is somewhere
between the two and mark the mean position on your desk. Then you draw a
line through it that corresponds to the major extent of the motion of your
hands, and write 'eigenvector 1' along it. You add a line through the
average position, perfectly perpendicular to the first, and write
'eigenvector 2' along it. Now you can project every position of your hands
onto your desk, giving it an 'eigenvector 1' coordinate (or score) and an
'eigenvector 2' coordinate (or score). You notice that it's only part of
the total motion, as you neglect the height, which will be a third line,
perpendicular to the desk.

You can look at it a bit differently and say that your desk is the subspace
of your real space, spanned by the two perpendicular vectors, which
together describe most of your hand's motion.

I hope this makes some sense :)

Cheers,

Tsjerk





On Mon, Mar 9, 2015 at 2:33 AM, Brett <brettliu123 at 163.com> wrote:

> Dear All,
>
> Recently I have read a gromacs related article which contain a sentence
> "Trajectories pojected on the first two eigenvectors". Will you please tell
> me the meaning of "eigenvector" and "Trajectories pojected on the first two
> eigenvectors"? Will you please also explain it to me using common-used
> words simple as desk, meal, earth, etc?
>
> Brett
>
>
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-- 
Tsjerk A. Wassenaar, Ph.D.