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The problem of solving approximately in the least squares sense an overdetermined linear system of equations with complex valued coefficients is considered, where the elements of the solution vector are constrained to have the same phase. A direct solution to this problem is given in [Linear Algebra and Its Applications, Vol. 433, pp. 1719-1721]. An alternative direct solution that reduces the problem to a generalized eigenvalue problem is derived in this paper. The new solution is related to generalized low-rank matrix approximation and makes possible one to use existing robust and efficient algorithms.

On the Complex Least Squares Problem with Constrained Phase