| 矩阵方程AX=B的转动不变解及其最佳逼近 |
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| 引用本文： | 张湘林,彭振赟.矩阵方程AX=B的转动不变解及其最佳逼近[J].数学理论与应用,2007,27(4):34-38. |
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| 作者姓名： | 张湘林 彭振赟 |
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| 作者单位： | 湖南科技大学数学与计算科学学院，湖南科技大学数学与计算科学学院 湘潭，411201，湘潭，411201 |
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| 摘 要： | 利用矩阵的广义逆、奇异值分解、张量积和拉直算子,给出了矩阵方程AX=B有转动不变解的充分必要条件及有解时通解的表达式;给出了矩阵方程解集合中与给定矩阵的最佳逼近解的表达式.
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| 关 键 词： | 矩阵方程 转动不变解 最佳逼近 |
The rotation invariable solution of matr4x equation AX=B and its optimal approximation |
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| Zhang Xianglin Peng Zhenyun.The rotation invariable solution of matr4x equation AX=B and its optimal approximation[J].Mathematical Theory and Applications,2007,27(4):34-38. |
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| Authors: | Zhang Xianglin Peng Zhenyun |
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| Abstract: | By using the generalized inverse,singular value decomposition,tensorproduct and draw operator of matrices,the sufficient and necessary conditions for the existence of and the general expressions for matrix equation AX =B has a rotation invariable solution are derived.In addition,in the solution set of the matrix equation,the unique optimal approximation solution to a given matrix in Frobenius norm is driven. |
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| Keywords: | Matrix equation rotation invariable matrix matrix norm |
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