| 求解矩阵方程AXBT+CYDT=T的一般解 |
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| 引用本文： | 卢俊峰.求解矩阵方程AXBT+CYDT=T的一般解[J].浙江大学学报(理学版),2007,34(4):361-363. |
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| 作者姓名： | 卢俊峰 |
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| 作者单位： | 浙江大学,数学系,浙江,杭州,310027;浙江工商大学,统计与数学学院,浙江,杭州,310018 |
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| 摘 要： | 对于矩阵方程AXB^T＋CYD^T=T，将其作为在列分块E=A,C]和F=B，D]下EZF^T的块对角约束问题，其中Z=diag（X,Y）．通过QR和CS分解，从无约束矩阵方程EZF^T=T的通解中得到相应块对角解的简洁表达式．
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| 关 键 词： | 矩阵方程 QR分解 CS分解 |
| 文章编号： | 1008-9497(2007)04-361-03 |
| 修稿时间： | 2006-01-12 |
General solutions of matrix equation AXBT+CYDT=T |
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| LU Jun-feng.General solutions of matrix equation AXBT+CYDT=T[J].Journal of Zhejiang University(Sciences Edition),2007,34(4):361-363. |
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| Authors: | LU Jun-feng |
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| Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, China; 2. College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China |
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| Abstract: | The matrix equation AXBT+CYDT=T is considered as the block diagonal constrained problem of EZFT=T with the column blocks E= and F=,where Z=diag(X,Y).By means of QR and CS decompositions,simple representations of block diagonal solutions to matrix equation EZFT=T are obtained from the general solutions to its unconstrained problem. |
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| Keywords: | matrix equation QR decomposition CS decomposition |
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