[R] A question about positive definite matrix

[rlearner309]

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.
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