The symmetric linear matrix equation
André C. M. Ran, Martine Reurings · Electronic Journal of Linear Algebra · 2002
Abstract. In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrixequations X −A ∗ 1 XA1 −...−A ∗ mXAm = Q and X +A ∗ 1 XA1 +...+ A ∗ mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given. Key words. Linear matrixequation, Positive definite solutions, Uniqueness of solutions. AMS subject classifications. 15A24