A formula for the solution of the matrix equation AX+XB=C
Abigail Ward · International Journal of Mathematical Education in Science and Technology · 1989
The Sylvester matrix equation AX+ XB = C is important in several branches of science and technology. It occurs, for example, as an ‘auxiliary equation’ to some of the differential equations of control theory. The method used here is based on the technique developed by Lacoss and Shakal. However, the formula given below is much more general than that of Lacoss and Shakal and deals with the case in which their formula fails.