Nonnegative-definite and positive-definite solutions to the matrix equationAXA*=B – revisited Original Research Article

The general Hermitian nonnegative-definite solution to the matrix equation AXA*=B is established in a form which can be viewed as a corrected version of that derived by C.G. Khatri and S.K. Mitra (SIAM J. Appl. Math. 31 (1976) 579–585) and an alternative version to that derived by J.K. Baksalary (Linear and Multilinear Algebra 16 (1984) 133–139). The new representation admits an easy way to obtain solutions of minimal and maximal rank, respectively.