| 矩阵方程AXA^T＋BYB^T=C的亚正定解 |
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| 引用本文： | 潘秋华.矩阵方程AXA^T＋BYB^T=C的亚正定解[J].安徽师范大学学报(自然科学版),2008,31(5). |
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| 作者姓名： | 潘秋华 |
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| 作者单位： | 江苏科技大学,数理系,江苏,镇江,212003 |
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| 摘 要： | 利用矩阵对的广义奇异值分解(GSVD),讨论了矩阵方程AXAT BYBT=C关于亚正定矩阵X、Y有解的充要条件,其中A,B,C是给定的矩阵,在有解时给出了解的通式.
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| 关 键 词： | 矩阵方程 矩阵分解 亚正定矩阵 通解 |
The Subpositive Definite Solutions of Matrix Equation AXAT+BYBT=C |
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| PAN Qiu-hua.The Subpositive Definite Solutions of Matrix Equation AXAT+BYBT=C[J].Journal of Anhui Normal University(Natural Science Edition),2008,31(5). |
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| Authors: | PAN Qiu-hua |
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| Abstract: | Applying the generalized singular value decompositions(GSVD) of matrices,a necessary and sufficient condition for matrix equation AXAT BYBT=C having subpositive definite solution is discussed,where A,B,C is given,and the explicit representation of generalized solution is given. |
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| Keywords: | matrices equations matrices decompositions subpositive definite solutions generalized solutions |
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