The Explicit Solution To Matrix Equation AX+XB=C And Its Applications

Almost all of the existing results on the explicit solutions to matrix equationAX + XB = C are obtained under the condition that A and B have no eigenvalues in common.In this paper ,we give the explicit solution to the matrix equation ,what is more ,we obtain more simple explicit solution when between A(A) and /l(5) satisfysome condition .According to conclusion above ,we not only obtain the general solutions to the matrix commuting with matrix A, but also give an explicit formulae for the minimurn-norm least-square solutions to matrix equation AX + YB= E andequations . Furthermore, some examples are given to testify correspondingtheorems.