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On hermitian positive definite solutions of a type of nonlinear matrix equations

Hongkui Li, Xueting Liu

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Abstract

In this paper, the Hermitian positive definite solutions of the matrix equation X + A* X-qA = I are studied, where A is an n times n nonsingular matrix. We give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on them, some properties and two equivalent equations of X + A* X-qA = I are presented when the matrix equation has a Hermitian positive definite solution.

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What this paper is about

In this paper, the Hermitian positive definite solutions of the matrix equation X + A* X-qA = I are studied, where A is an n times n nonsingular matrix. We give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on them, some properties and two equivalent equations of X + A* X-qA = I are presented when the matrix equation has a Hermitian positive definite solution.

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Available abstract

In this paper, the Hermitian positive definite solutions of the matrix equation X + A* X-qA = I are studied, where A is an n times n nonsingular matrix. We give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation. And based on them, some properties and two equivalent equations of X + A* X-qA = I are presented when the matrix equation has a Hermitian positive definite solution.

Key concepts: Hermitian matrix, Invertible matrix, Positive-definite matrix, Matrix (chemical analysis), Matrix algebra, Mathematics, Pure mathematics, Physics

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