On solvability of the matrix equation AX+YB=C over principal ideal domains - Prokip, Volodymyr M. (Modeling, Control and Information Technologies: Proceedings of International scientific and practical conference, 2025)
In this communication we present conditions for solvability of the matrix equation AX + YB = C over the ring of integers . The necessary and sufficient conditions for the solvability of this equation in terms of the Smith normal forms of the matrices A and B are given. The conditions under which this equation has a minimal solution are also given.