| 矩阵方程 (A*XA， B *XB ) =(C， D)有Hermite部分是
半正定的解与Hermite半正定解的条件 |
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| 引用本文： | 周立仁.矩阵方程 (A*XA， B *XB ) =(C， D)有Hermite部分是
半正定的解与Hermite半正定解的条件[J].湖南工业大学学报,2008,22(1):47-52. |
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| 作者姓名： | 周立仁 |
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| 作者单位： | 湖南理工学院数学系,湖南,岳阳,414006 |
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| 摘 要： | 研究了复矩阵方程(A*XA,B*XB)=(C,D)有Hermite部分是半正定的解与Hermite半正定解的可解性条件。利用广义奇异值分解,导出了矩阵方程(A*XA,B*XB)=(C,D)有Hermite部分是半正定的解、Hermite半正定的解的充分必要条件,同时给出了解的通式。
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| 关 键 词： | 矩阵方程 Hermite半正定 广义奇异值分解 matrix equation:Hermite positive semidefinite:generalized singular value decomposition 矩阵方程 Hermite 半正定解 可解性条件 Matrix Equation Solutions Positive Semidefinite Conditions forms general solution sufficient conditions solvability derived generalized singular decomposition complex matrix equation solutions positive semidefinite |
| 文章编号： | 1673-9833（2008）01-0047-06 |
| 收稿时间： | 2007-03-19 |
The Solvability Conditions with Hermite Part Positive Semidefinite and Hermite Positive Semidefinite Solutions of the Matrix Equation (A*XA, B*XB)=(C, D) |
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| Zhou Liren.The Solvability Conditions with Hermite Part Positive Semidefinite and Hermite Positive Semidefinite Solutions of the Matrix Equation (A*XA, B*XB)=(C, D)[J].Journal of Hnnnan University of Technology,2008,22(1):47-52. |
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| Authors: | Zhou Liren |
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| Abstract: | The complex matrix solutions with Hermite part positive semidefinite and Hermite positive semidefinite for the matrix equation(A*XA,B*XB)=(C,D) is investigated.The necessary and sufficient conditions for the solvability of such solutions are derived by using the generalized singular value decomposition.The forms of general solution are also given out. |
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| Keywords: | matrix equation Hermite positive semidefinite generalized singular value decomposition |
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