Dear all,
Suppose U and V are unitary matrix, A and B are positive definite,
Does:
$UAU^{-1} < VBV^{-1}$
implies $A< B$
and vice versa?
2
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$\begingroup$ What do you mean with $A<B$? Are you comparing term by term? Moreover, Do $U$ and $V$ diagonalize $A$ and $B$ respectively and you are comparing the diagonal terms? $\endgroup$– DoxCommented Aug 16, 2012 at 15:47
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$\begingroup$ I mean by A < B is (B-A) > 0 or (B-A) is positive definite. U and V not necessarily diagonalize A and B, just to make them block diagonal. Thanks. $\endgroup$– hayuCommented Aug 16, 2012 at 15:59
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