On a transformation of the ∗-congruence Sylvester equation for the least squares optimization

The ★-congruence Sylvester equation is the matrix equation AX+X⋆B=C, where A∈Fm×n, B∈Fn×m and C∈Fm×m are given, whereas X∈Fn×m is to be determined. Here, F=R or C, and ⋆=T (transposed) or ∗ (conjug...