  Given a pair of matrices X and B and an appropriate class of structured
matrices S, we provide a complete solution of the structured inverse
least-squares problem $min_{A\in_S} \|AX-B\|_F$. Indeed, we determine all
solutions of the structured inverse least squares problem as well as those
solutions which have the smallest norm. We show that there are infinitely many
smallest norm solutions of the least squares problem for the spectral norm
whereas the smallest norm solution is unique for the Frobenius norm.
