a new approximation to the solution of the linear matrix equation axb = c

It is well-known that the matrix equations play a significant role in several applications 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 homotopy 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 modified method.