[Fis]: Re: symmetry and information theory

From: Michel Petitjean <[email protected]>
Date: Mon 17 May 2004 - 10:57:52 CEST

To: <fis@listas.unizar.es>
Subject: [Fis]: Re: symmetry and information theory

Dear Loet,

You said:
> For those of you interested in the relation between information theory
> and symmetry, it may be interesting to study the test on the symmetry in
> matrices provided by Solomon Kullback, Information Theory and
> Statistics, (New York: Wiley, 1959). Perhaps, it is possible to
> generalize from there to a test for symmetry more generally.

Thanks for the pointer. There are many ways to test symmetry of a square
matrix A, the simplest being to see if some norm of A-transpose(A) is
close to zero (compared to the norm of A or transpose(A)). More generally,
many symmetry tests and measures were proposed by mathematicians
and scientists, for sets of points, distributions,... I did a review
of this topic last year: Entropy 2003, 5[3], 271-312. It can be
downloaded (free) from: http://www.mdpi.net/entropy/list03.htm
in pdf format: http://www.mdpi.net/entropy/papers/e5030271.pdf
or postscript: http://www.mdpi.net/entropy/papers/e5030271.ps
The case of indirect symmetry is quite different from the case of
direct symmetry (see the general theory in section 6 of the paper).
The relations with order/disorder are evoked, but not the relations
with information. These latter are of much interest here, and so
I would like to hear about them.

Michel Petitjean Email: petitjean@itodys.jussieu.fr
Editor-in-Chief of Entropy entropy@mdpi.org
ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
1 rue Guy de la Brosse Phone: +33 (0)1 44 27 48 57
75005 Paris, France. FAX : +33 (0)1 44 27 68 14
http://www.mdpi.net http://www.mdpi.org
http://petitjeanmichel.free.fr/itoweb.petitjean.html
http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html
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Received on Mon May 17 10:59:51 2004

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