Zhao, Linlin Some inequalities for the nonlinear matrix equations. (English) Zbl 1273.15006 Math. Inequal. Appl. 16, No. 3, 903-910 (2013). Summary: The nonlinear matrix equations \(X \pm A^\ast X^{-1}A = \mathcal Q\) have many applications in control theory, dynamic programming and statistics. In the present work, by using some related matrix equalities and linear algebraic techniques, we propose some trace and determinant inequalities for the solution of the above nonlinear matrix equations. Furthermore, we give some inequalities for the eigenvalues of their solutions. Cited in 1 ReviewCited in 1 Document MSC: 15A15 Determinants, permanents, traces, other special matrix functions 15A18 Eigenvalues, singular values, and eigenvectors 15A24 Matrix equations and identities Keywords:nonlinear matrix equation; trace; determinant; eigenvalue; positive definite solution PDFBibTeX XMLCite \textit{L. Zhao}, Math. Inequal. Appl. 16, No. 3, 903--910 (2013; Zbl 1273.15006) Full Text: DOI