A note on positive definite solution of matrix equation X+M^*X^–1M–N^*X^–1N=1

Abstract

In this note, we argue that Theorem 2.2 and its proof in Duan XF, et al. [Positive definite solution of a class of nonlinear matrix equation. Linear and Multilinear Algebra. 2014;6:839–852] is seriously flawed and prove a new result based on Brouwer’s fixed-point theorem.

Keywords:

• nonlinear matrix equation
• stochastic control
• positive definite solution

AMS Subject Classifications:

• 15A24
• 65H05

Acknowledgements

The author would like to express his gratitude to the referees for providing very useful suggestions.

Notes

No potential conflict of interest was reported by the authors.