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?
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? 

closed as too localized by Deane Yang, Bill Johnson, Mark Sapir, Suvrit, Mark Meckes Aug 16 '12 at 17:02This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


No: think of the case of $A$, $B$ diagonal; $U$ identity, and $V$ a permutation operator. 

