Article ID Journal Published Year Pages File Type
4602756 Linear Algebra and its Applications 2008 15 Pages PDF
Abstract

In this paper, the existence of Hermitian positive definite solutions of the general nonlinear matrix equation Xs+A∗X-tA=Q is studied systematically and deeply. A new estimate of Hermitian positive definite solutions is derived. Based on a fixed point theorem, some new sufficient conditions and new necessary conditions for the existence of Hermitian positive definite solutions are obtained. In the end, a necessary and sufficient condition for the existence of a Hermitian positive definite solution is proved.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory