Least Squares Approximation by Real Normal Matrices with Speci ed Spectrum

The problem of best approximating a given real matrix in the Frobenius norm by real normal matrices subject to a prescribed spectrum is consid ered The approach is based on using the projected gradient method The projected gradient of the objective function on the manifold of constraints can be formulated explicitly This gives rise to a descent ow that can be followed numerically The explicit form also facilitates the computation of the second order optimality condition from which some interesting proper ties of the stationary points are related to the well known Wielandt Ho man Theorem