I have a hermitian matrix $A$ which can be diagonalized: $$A=UDU^+,$$ where U is the unitary matrix and D is the diagonal matrix. Next, I have a completely positive transformation over it, which is introduced with the set of matrices $\{L_j\}$ so that $$\tilde{A}=\sum_j{L_jAL_j^+},$$ where $\tilde{A}$ is again the hermitian matrix with diagonalization: $$\tilde{A}=\tilde{U}\tilde{D}\tilde{U}^+.$$ The question is: can $\tilde{U}$ and $\tilde{D}$ be somehow expressed via $U$, $D$ and $\{L_j\}$?
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1$\begingroup$ Of course: from $U$ and $D$ you compute $A$, with that and the $L_j$ you get $\widetilde{A}$, and from that you get (non-uniquely, of course) $\widetilde{D}$ and $\widetilde{U}$. But if you want a much simpler way than that, it's rather unlikely. $\endgroup$– Robert IsraelCommented Apr 21, 2016 at 21:03
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$\begingroup$ @RobertIsrael, I would like to get an analytical result but event in the case of 2x2 matrix it seems to be hardly resolvable, so I'm looking for some convinient matrix expression $\endgroup$– KrivoiCommented Apr 21, 2016 at 21:38
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