The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation AXA*=B

A simple representation of the general rank-constrained Hermitian nonnegative-definite (positive-definite) solution to the matrix equation AXA*=B is derived. As medium steps, the general Hermitian solution and the general Hermitian nonnegative-definite (positive-definite) solution to the matrix equation are also obtained. The proposed approach is different from those which we have known, and possesses good numerical reliability since it mainly involves only two singular value decompositions and inverses of two positive-definite diagonal matrices. The presented example illustrates the proposed approach.