Ran, André C. M.; Reurings, Martine C. B. The symmetric linear matrix equation. (English) Zbl 1002.15015 Electron. J. Linear Algebra 9, 93-107 (2002). The authors study solutions to the equations \[ X \pm (A_1^*XA_1 +\ldots + A_m^*XA_m) =Q \] which occur in the Newton method applied to algebraic Riccati equations. Conditions are found for these equations to have unique solutions, and an explicit formula is given in the case when there is a unique positive definite solution. Reviewer: Kim Hang Kim (Montgomery) Cited in 17 Documents MSC: 15A24 Matrix equations and identities Keywords:linear matrix equation; uniqueness; positive definite solution PDF BibTeX XML Cite \textit{A. C. M. Ran} and \textit{M. C. B. Reurings}, Electron. J. Linear Algebra 9, 93--107 (2002; Zbl 1002.15015) Full Text: DOI EuDML EMIS OpenURL