Abstract
In this paper, the matrix equation $$X+\sum _{i=1}^{m}A_{i}^*X^{-q_{i}}A_{i}=I$$ with $$0<q_{i}\le 1$$ is investigated. Based on the integral representation of matrix functions and the properties of Kronecker product, we discuss the uniqueness of the Hermitian positive definite (HPD) solution of the above equation. Some properties of the HPD solution are obtained.
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