Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations. (19th October 2009) - Zhao, Wenling; Li, Hongkui; Liu, Xueting; Xu, Fuyi
Abstract : We study the Hermitian positive definite solutions of the nonlinear matrix equation X + A ∗ X − 2 A = I, where A is an n × n 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 X + A ∗ X − 2 A = I are presented while the matrix equation has a Hermitian positive definite solution.