On the matrix equation X + ATX-1A = I

Xingzhi Zhan; Jianjun Xie

doi:10.1016/0024-3795(95)00120-4

On the matrix equation X + A^TX^-1A = I

Xingzhi Zhan^*
, Jianjun Xie

^*Corresponding author for this work

Fudan University

Research output: Contribution to journal › Article › peer-review

101 Scopus citations

Abstract

Simple necessary and sufficient conditions for the matrix equation X + A^TX^-1A = I to have a positive definite solution are given. These conditions are used to explain some properties of the equation and to obtain new information. Finally we prove a conjecture on the extremal solutions.

Original language	English
Pages (from-to)	337-345
Number of pages	9
Journal	Linear Algebra and Its Applications
Volume	247
DOIs	https://doi.org/10.1016/0024-3795(95)00120-4
State	Published - 1 Nov 1996
Externally published	Yes

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title = "On the matrix equation X + ATX-1A = I",

abstract = "Simple necessary and sufficient conditions for the matrix equation X + ATX-1A = I to have a positive definite solution are given. These conditions are used to explain some properties of the equation and to obtain new information. Finally we prove a conjecture on the extremal solutions.",

author = "Xingzhi Zhan and Jianjun Xie",

year = "1996",

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doi = "10.1016/0024-3795(95)00120-4",

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AB - Simple necessary and sufficient conditions for the matrix equation X + ATX-1A = I to have a positive definite solution are given. These conditions are used to explain some properties of the equation and to obtain new information. Finally we prove a conjecture on the extremal solutions.

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DO - 10.1016/0024-3795(95)00120-4

M3 - 文章

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

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On the matrix equation X + A^TX^-1A = I

Abstract

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