A new approximation to the solution of the linear matrix equation AXB = C

It is well-known that the matrix equations play a signicant role in several ap- plications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the ho- motopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB = C. Furthermore, the conditions will be explored to check the convergence of the homotopy series. Numerical examples are also adapted to illustrate the properties of the modied method.