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

^*此作品的通讯作者

Fudan University

科研成果: 期刊稿件 › 文章 › 同行评审

102 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	337-345
页数	9
期刊	Linear Algebra and Its Applications
卷	247
DOI	https://doi.org/10.1016/0024-3795(95)00120-4
出版状态	已出版 - 1 11月 1996
已对外发布	是

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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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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

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

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