Structured Procrustes problem

Let SS be a class of structured matrices. Given a pair of matrices X and B, we consider the structured Procrustes problem (SPP)A=arg⁡minG∈S⁡‖GX−B‖F and provide a complete solution when SS is either a Jordan algebra or a Lie algebra associated with an orthosymmetric scalar product. We characterize and determine all solutions of the structured Procrustes problem as well as those solutions which have the smallest norm. We show that, for the spectral norm, there may be infinitely many smallest norm solutions of the structured Procrustes problem whereas, for the Frobenius norm, the smallest norm solution is unique.