| THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION——B~TXB = D ON LINEAR MANIFOLDS |
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| 引用本文： | 邓远北,胡锡炎,张磊.THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION——B~TXB = D ON LINEAR MANIFOLDS[J].高等学校计算数学学报(英文版),2003,12(2). |
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| 作者姓名： | 邓远北 胡锡炎 张磊 |
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| 作者单位： | College of Mathematics and Econometrics，Hunan UniVersity，Challgsha 410082 PRC，College of Mathematics and Econometrics，Hunan University，Changsha 410082 PRC，Hunan Computing Center，Changsha 410082 PRC |
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| 基金项目： | This work was supposed by the National Nature Science Foundation of China |
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| 摘 要： | This paper discusses the solutions of the linear matrix equation B~T XB=D on some linear manifolds. Some necessary and sufficient conditions for the existence of the solution and the expression of the general solution are given. And also some optimal approximation solutions are discussed.
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THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION BTXB=D ON LINEAR MANIFOLDS |
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| Deng Yuanbei College of Mathematics and Econometrics,Hunan University,Changsha ,PRC.
Hu Xiyan College of Mathematics and Econometrics,Hunan University,Changsha ,PRC. Zhang Lei Hunan Computing Center,Changsha ,PRC..THE SYMMETRIC AND SYMMETRIC POSITIVE SEMIDEFINITE SOLUTIONS OF LINEAR MATRIX EQUATION BTXB=D ON LINEAR MANIFOLDS[J].Numerical Mathematics A Journal of Chinese Universities English Series,2003,12(2). |
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| Authors: | Deng Yuanbei College of Mathematics and Econometrics Hunan University Changsha PRC
Hu Xiyan College of Mathematics and Econometrics Hunan University Changsha PRC Zhang Lei Hunan Computing Center Changsha PRC |
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| Institution: | 1. College of Mathematics and Econometrics,Hunan University,Changsha 410082,PRC
2. Hunan Computing Center,Changsha 410082,PRC |
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| Abstract: | This paper discusses the solutions of the linear matrix equation BTXB = D on some linear manifolds. Some necessary and sufficient conditions for the existence of the solution and the expression of the general solution are given. And also some optimal approximation solutions are discussed. |
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| Keywords: | matrix equation matrix norm linear manifold symmetric (positive semidefinite) matrix optimal approximation |
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