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On Hermitian Positive Definite Solutions of a Type of Nonlinear Matrix Equations and Application

In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation are studied. We present some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on the necessary and sufficient conditions, some properties when the matrix equation has a Hermitian positive definite solution, and an iterative method for finding the maximal solution are given.