ELA, Volume 9, pp. 93-107, May 2002, abstract.
The Symmetric linear matrix equation
Andre C.M. Ran and Martine C.B. Reurings
In this paper sufficient conditions are derived
for the existence of unique and positive definite
solutions of the matrix equations
X-A_1^*XA_1- ... -A_m^*XA_m = Q
and
X+A_1^*XA_1+ ... +A_m^*XA_m = Q.
In the case there is a unique solution which is
positive definite an explicit expression for
this solution is given.