The Hermitian Positive Definite Solution of Nonlinear Matrix Equations

Abstract

In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation $X+A* X^{-2} A+I$. Suppose $X$ is a Hermitian positive definite solution of this equation. We discuss the relation between $X$ and $A$ by the eigenvalue and eigenvector of $X$ and $A$ respectively.