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

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  • Wenling Zhao
  • Hongkui Li
  • Xueting Liu
  • Fuyi Xu

Abstract

We study the Hermitian positive definite solutions of the nonlinear matrix equation , where is an 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 are presented while the matrix equation has a Hermitian positive definite solution.

Suggested Citation

  • Wenling Zhao & Hongkui Li & Xueting Liu & Fuyi Xu, 2009. "Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-13, October.
    • Handle: RePEc:hin:jnlmpe:672695
    DOI: 10.1155/2009/672695
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