Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations

Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations

We study the Hermitian positive definite solutions of the nonlinear matrix equation X+A∗X−2A=I, where A is an n×n nonsingular 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 s...

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Veröffentlicht in:Mathematical problems in engineering 2009, Vol.2009 (2009), p.1-13
Hauptverfasser: Zhao, Wenling, Li, Hongkui, Liu, Xueting, Xu, Fuyi
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Liu, Xueting
Xu, Fuyi
description We study the Hermitian positive definite solutions of the nonlinear matrix equation X+A∗X−2A=I, where A is an n×n nonsingular 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 of X+A∗X−2A=I are presented while the matrix equation has a Hermitian positive definite solution.
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title Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations
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