Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 5, pp 1171–1184

# Solvability for a Nonlinear Matrix Equation

• J. Li
• Y. H. Zhang
Original Paper

## 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.

## Keywords

Nonlinear matrix equation Hermitian positive definite solution Kronecker product Integral representation of matrix functions

## Mathematics Subject Classification

Primary 15A24 Secondary 15A48

## Notes

### Acknowledgements

The authors are grateful to anonymous referees for their valuable comments and suggestions, which greatly improve the original manuscript of this paper. The work was supported in part by National Nature Science Foundation of China (11601277).

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