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 eigenstructure,... 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).
######################################################################
Attention:
This e-mail message is privileged and confidential. If you are not the
intended recipient please delete the message and notify the sender.
Any views or opinions presented are solely those of the author.
This e-mail has been scanned and cleared by MailMarshal www.marshalsoftware.com
######################################################################
pos def.pdf
Description: Adobe PDF document
______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
