The reflexive re-nonnegative definite solution to a quaternion matrix equation

In this paper a necessary and sufficient condition is established for the existence of the reflexive re-nonnegative definite solution to the quaternion matrix equation AXA* = B, where * stands for conjugate transpose. The expression of such solution to the matrix equation is also givenfurthermore, a necessary and sufficient condition is derived for the existence of the general re- nonnegative definite solution to the quaternion matrix equation A(1)X(1)A(1)* + A(2)X(2)A(2)* = B. The representation of such solution to the matrix equation is given.