If you have complex matrix M, how can you decompose M into three matrices, A, B, C? They are all complex and n by n matrices.
Additional information of matrices A, B, C is as follows. A and C are symmetric (possibly hermitian), unitary B has only diagonal components (or mainly close-diagonal components).
Obviously, this is an underdetermined problem. I thought this is intractable. But, I just wondered if there exist any ways to tackle this problem (or some approximation/relaxation) I'd appreciate your help!