Real iterative algorithms for solving a complex matrix equation with two unknowns

This paper discusses two iterative solutions for a complex matrix equation with two unknowns of the form A1VB1+C1WD1+A2V¯B2+C2W¯D2=E. When this matrix equation is consistent, by using a real inner product in complex matrix space as a tool, solutions for any initial matrices V1,W1 may be determined in finite iterative steps without round-off errors. In the same equation, we also consider a real iterative algorithm using a real representation of a complex matrix as a tool. Some lemmas and theorems are given and proven in the context of iterative solutions. A numerical example is provided to show the efficacy of the suggested algorithms.