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.
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页数：7
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