Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation X + Σi=1m AiT Xδi Ai = I

被引：0

作者：

El-Shazly, Naglaa M. ^{[1
]}

机构：

[1] Menoufia Univ, Dept Math, Fac Sci, Shibin Al Kawm, Egypt

来源：

JOURNAL OF APPLIED MATHEMATICS | 2013年

关键词：

D O I：

10.1155/2013/537520

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper necessary and sufficient conditions for the matrix equation X + Sigma(m)(i=1) A(i)(T) X-delta i A(i) = I to have a positive definite solution X are derived, where -1 < delta(i) < 0, I is an n x n identity matrix, A(i) are n x n nonsingular real matrices, and m is an odd positive integer. These conditions are used to propose some properties on the matrices A(i), i = 1, 2, ... , m Moreover, relations between the solution.. and the matrices A(i) are derived.

引用

页数：7

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