Geodesic
The symmetric linear matrix equation
The electronic journal of linear algebra, Tome 9 (2002), pp. 93-107.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X -A*1XA1 -. . .-A*mXAm = Q and X +A*1XA1 +. . .+ A*mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.
Classification : 15A24
Keywords: linear matrix equation, positive definite solutions, uniqueness of solutions 
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     title = {The symmetric linear matrix equation},
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Ran, André C.M.; Reurings, Martine C.B. The symmetric linear matrix equation. The electronic journal of linear algebra, Tome 9 (2002), pp. 93-107. http://geodesic.mathdoc.fr/item/ELA_2002__9__a16/