Some inequalities for the nonlinear matrix equations

Abstract

The nonlinear matrix equations X ±A∗X−1A = 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. Mathematics subject classification (2010): 15A15, 15A18, 15A24.