On hermitian positive definite solutions of a type of nonlinear matrix equations
Hongkui Li, Xueting Liu · 2009
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.