The Solution To The Equation AX+f(X)B=C And The Application Of The Solving Method

Matrix is an important basic concept in mathematics. It is one of the important object of study in algebra and it is an indispensable tool in the research and application of mathematics and other areas. The operator equation is an important part of functional analysis and it is an active branch of the modern mathematics. The theory of matrix and operator had a further development. At present, they have developed into physics, control theory, robotics, biology, economics and other disciplines who have a wide range of application in mathematics branch. In this paper, we study the general solution to the equation of AX+f(X)B=C with f(X) is XT, X*and the X is unknown. We proposed two methods to solve the equation AX+f(X)B=C. The first one is applied when the parameters are matrices. In this case, we make the equation linearization, then use the method of solving the system of linear equations to solve the equation. The second one is that when we extend the equation to the infinite dimensional settings, we will consider the equations by the Moore-Penrose inverse of the operator. On the other hand, the method has an important application in solving the solution to the equation of AXB+EX*F=C which is in the special conditions. At the same time, some useful conclusions are made.