Let $A$ and $B$ be semidefinite positive matrices. In which case is the following relation correct please?
$$ Tr(A^{-1})\geq Tr(B^{-1})\implies Tr(A)\leq Tr(B), $$ where $Tr(A)$ means the trace of the matrix $A$.
what does inequality between traces of inverse of matrices imply?
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linear-algebra
matrices
trace
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0try some diagonal matrices, 2 by 2 and 3 by 3. – 2017-01-14