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Subject: Re: [R] A question about positive definite matrix
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--- Begin Message ---
On 20/10/2008, at 5:26 PM, rlearner309 wrote:
I know, this is a forum about R. But I am so desperate of this
problem (BTW,
anyone knows any good Statistics/Math forum to post question like
this?):
A and B are both n x n positive definite matrix.
Denote A > B, if A - B is positive definite.
I know this is true: if A > B, then A^{-1} < B^{-1}. But how to
prove this?
I tried to diagonalize A and B, but since they can have different
eigen
structure,... I am stuck here.
Thanks a lot for any help here.
Your problem intrigued me; I tried to prove the result; couldn't;
asked a clever
mate; he couldn't; he asked some clever mates, who finally came up
with the proof
that I have attached in pdf form.
(Anyone who's interested: If the attachment gets removed by the list,
send me email
and I'll send the pdf file to you directly.)
cheers,
Rolf Turner
P. S. ``WLU'' (in the pdf file) means Wilfrid Laurier University
(Waterloo, Ontario, Canada).
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pos def.pdf
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