The Hermitian Positive Definite Solution of Some Matrix Equations
Xuetting Liu, Peiyu Wei · 2009
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-2A = I are studied. We discuss the relation between X and A by the eigenvalue and eigenvector of X and A respectively, and the property of numerical range of A . An iterative method for obtaining positive definite solutions of the equation is constructed.