Copyright © 2009 Wenling Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.