On constructing Hermitian unitary matrices with prescribed moduli 1

Abstract

The problem of reconstructing the phases of a unitary matrix with prescribed moduli is of a broad interest to people working in many applications, e.g in the circuit theory, phase shift analysis, multichannel scattering, computer science (e.g in the theory of error correcting codes, design theory). We propose efficient algorithms for computing Hermitian unitary matrices for given symmetric bistochastic matrices A(n × n) for n = 3 and n = 4. We mention also some results for matrices of arbitrary size n.