A comprehensive theory of the matrix linear equation AX + XB = C is presented. The equation is viewed as a vector equation LX = C in the vector space of all m × n matrices. As the main result, two ...

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 ...