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Solvability for a Nonlinear Matrix Equation

  • J. Li
  • Y. H. Zhang
Original Paper
  • 3 Downloads

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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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsShandong UniversityWeihaiPeople’s Republic of China

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