摘要
In this paper, we consider the positive semidefinite solution of the matrix equation (AT X A, BT X B) - (C, D). A necessary and sufficient condition for the existence of such solution is derived using the generalized singular value decomposition.The general forms of positive semidefinite solution are given.
In this paper,we consider the positive semidefinite solution of the matrixequation (A^TXA, B^TXB) = (C, D). A necessary and sufficient condition for the ex-istence of such solution is derived using the generalized singular value decomposition.The general forms of positive semidefinite solution are given.
基金
Partially supported by the National Natural Science Foundation of China(No10071035) and the Doctor Foundation of Hunan Normal University.
关键词
积极半确定解
通用单值分解
矩阵方程
平方根
positive semidefinite matrix
generalized singular value decomposition
matrix equation
