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Re: Multivariate pdf of a normal distribution


From: Gorazd Brumen
Subject: Re: Multivariate pdf of a normal distribution
Date: Sun, 06 Nov 2005 15:40:16 +0100
User-agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.7.12) Gecko/20050920


Hello Paul,


I don't know for sure that inv(r') == inv(r)' for r upper triangular. Numerically it is not the case in octave:

    octave:34> x = triu(rand(10)); norm(inv(x') - inv(x)')
    ans =  3.3466e-14

Assuming that it is, then

I think I have proven that this is the case (at least for upper
triangular matrices).
But perhaps it is the case actually for all invertible matrices, not only
for upper triangular ones.
If you want a proof I need a couple of minutes to latex it and I can
send it to you,
but maybe this is such an obvious fact, that it is in every algebra book
(maybe somebody knows).

Thanks a lot for the function.


Gorazd



--
Gorazd Brumen
Mail: address@hidden
WWW: http://valjhun.fmf.uni-lj.si/~brumen
PGP: Key at http://pgp.mit.edu, ID BCC93240



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