Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
C. G. Khatri, Sujit Kumar Mitra · SIAM Journal on Applied Mathematics · 1976
Necessary and sufficient conditions for existence and expressions for general Hermitian and nonnegative definite solutions are obtained for the following three systems of linear equations: (I) $AX = C$, (II) $AX = C,XB = D$, (III) $AXB = C$.