Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations
Wenling Zhao, Hongkui Li, Xueting Liu, Fuyi Xu · Mathematical Problems in Engineering · 2009
We study the Hermitian positive definite solutions of the nonlinear matrix equationX+A∗X−2A=I, whereAis ann×nnonsingular matrix. Some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation are given. However, based on the necessary and sufficient conditions, some properties and the equivalent equations ofX+A∗X−2A=Iare presented while the matrix equation has a Hermitian positive definite solution.