On the parametrisation of unitary matrices by the moduli of their elements (Q1317407)

The parametrisation of an \(n \times n\) unitary matrix by the moduli of its elements is not a well posed problem, i.e. there are continuous and discrete ambiguities which naturally appear. The paper shows that the continuous ambiguity is \((n-1) (n-3)\)-dimensional in the general case and \((n(n-3)/2)\)-dimensional in the symmetric case \(S_{ij}=S_{ji}\). Lower bounds on the number of discrete ambiguities are also given.