| 矩阵方程（AX，XB）=（C，D）和AXB=C的对称正定解 |
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| 引用本文： | 戴华.矩阵方程（AX，XB）=（C，D）和AXB=C的对称正定解[J].南京航空航天大学学报(英文版),1996(2). |
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| 作者姓名： | 戴华 |
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| 作者单位： | 南京航空航天大学理学院 |
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| 摘 要： | 讨论了矩阵方程（ＡＸ，ＸＢ）＝（Ｃ，Ｄ）和ＡＸＢ＝Ｃ的对称正定解。利用奇异值分解和广义奇异值分解导出了这些矩阵方程有对称正定解的充分必要条件，并且给出了一般对称正定解的表达式
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| 关 键 词： | 数值代数 矩阵 方程 对称正定解 |
SYMMETRIC POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATIONS (AX,XB)=(C,D) AND AXB=C |
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| Dai Hua College of Science,NUAA Yudao Street,Nanjing ,P. R. China.SYMMETRIC POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATIONS (AX,XB)=(C,D) AND AXB=C[J].Transactions of Nanjing University of Aeronautics & Astronautics,1996(2). |
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| Authors: | Dai Hua College of Science NUAA Yudao Street Nanjing P R China |
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| Institution: | Dai Hua College of Science,NUAA29 Yudao Street,Nanjing 210016,P. R. China |
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| Abstract: | The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold. |
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| Keywords: | numerical algebra matrix equation symmetric positive definite solution |
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