Pedro:
> Ok as far as I can see it's
> Category ID (class)
> Mean vector (each value is the average for the category in each band)
> 
> Var(b1;b1)
> Cov(b1,b2)  Var(b2;b2)
> Cov(b1,b3)  Cov(b2,b3)  Var(v3,v3)
> 
> it's this?

It would take me to perform a test with numbers and see what is what exactly. 
Maybe some math-grass-guru can explain quickly ;-)

> By the way, is in any place the inversion of the covariance matrix?

Hmm... are you looking for this (or relevant):
 
<http://trac.osgeo.org/grass/browser/grass/branches/releasebranch_6_4/imagery/i.gensig/check.c>

Nikos

ps: Maybe we can put this in the wiki after it is clear what is what

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