I have the following equation : $ \tilde{B} = U B U^{\dagger} $
I also know both $ B $ and $ \tilde{B} $ , I just want to find the matrix U, that gives me the transformation. I tried using LinearSolve, but I can't get it into the form required by that function. Is there another way to do that?
I must note that the condition that U be Unitary is ESSENTIAL. I make this remark because of the interesting solutions proposed below, none of which, however, gives a unitary matrix U.
Edit: If it is of any help, the two matrices B and $ \tilde B $ are two quantum density matrices.
Edit2: I also added the two matrices here: http://pastebin.com/s3B1T0HD
Chop[SchurDecomposition[mat, RealBlockDiagonalForm -> False]]
to both of your matrices, and check if the triangular (diagonal?) matrices produced are the same (up to roundoff and permutation). We can proceed after you do this. $\endgroup$