| 关于矩阵方程AXB-C=0的最佳逼近解的一个注记 |
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| 引用本文： | 宋传宁,许庆祥. 关于矩阵方程AXB-C=0的最佳逼近解的一个注记[J]. 上海师范大学学报(自然科学版), 2018, 47(1): 22-23 |
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| 作者姓名： | 宋传宁 许庆祥 |
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| 作者单位： | 上海师范大学 数理学院, 上海 200234,上海师范大学 数理学院, 上海 200234 |
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| 基金项目： | The National Natural Science Foundation of China (11671261) |
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| 摘 要： | 举反例说明：对于矩阵的2-范数,存在矩阵A,B和C,使得A†CB†不是矩阵方程AXB-C=0的最佳逼近解,其中A†和B†分别是A和B的Moore-Penrose逆.
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| 关 键 词： | Moore-Penrose逆 Frobenius 范数 2-范数 |
| 收稿时间： | 2017-02-25 |
A note on the best approximate solution of the equation AXB-C=0 |
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| Song Chuanning and Xu Qingxiang. A note on the best approximate solution of the equation AXB-C=0[J]. Journal of Shanghai Normal University(Natural Sciences), 2018, 47(1): 22-23 |
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| Authors: | Song Chuanning and Xu Qingxiang |
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| Affiliation: | Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China and Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | A counterexample is constructed which shows that with respect to the 2-norm,there exist matrices A,B and C such that A† CB† fails to be the best approximate solution of the equation AXB-C=0,where A† and B† are the Moore-Penrose inverses of A and B,respectively. |
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| Keywords: | Moore-Penrose inverse Frobenius norm 2-norm |
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