We study the matrix equation XA - AX = τ (X) in Mn (K), where τ is an automorphism of a field K of finite order k. A criterion under which this equation has a nontrivial solution is given. In case ...

Let SE denote the least-squares symmetric solution set of the matrix equation AX B = C, where A, B and C are given matrices of suitable size. To find the optimal approximate solution in the set SE to ...