Document Zbl 1151.15302

**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

Acta Sci. Nat. Univ. Pekin. 41, No. 1, 55-61 (2005).

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.

Cited in 1 Document

MSC:

15A24	Matrix equations and identities
15A23	Factorization of matrices

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an	internal document identifier
au	author, editor
ai	internal author identifier
ti	title
la	language
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ab	review, abstract
py	publication year
rv	reviewer
cc	MSC code
ut	uncontrolled term
dt	document type (j: journal article; b: book; a: book article)

a & b	logic and
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!ab	logic not
abc*	right wildcard
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**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

MSC:

Examples

Fields

Operators

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

MSC:

**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