## Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation $$X+A^* X^{-2}A=I$$.(Chinese)Zbl 1151.15302

Summary: The matrix equation $$X + A^* X-2 A = I$$ is studied. Some necessary and sufficient conditions for the existence of a positive definite solution of this equation are derived. Based on them, some properties of the coefficient matrix A are presented when the matrix equation has a positive definite solution.

### MSC:

 15A24 Matrix equations and identities 15A23 Factorization of matrices