Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations
نویسندگان
چکیده
We study the Hermitian positive definite solutions of the nonlinear matrix equation X A∗X−2A 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−2A I are presented while the matrix equation has a Hermitian positive definite solution.
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