| 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. |
| 关键词: Moore-Penrose逆 Frobenius 范数 2-范数 |
| DOI：10.3969/J.ISSN.1000-5137.2018.01.003 |
| 分类号: |
| 基金项目:The National Natural Science Foundation of China (11671261) |
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| A note on the best approximate solution of the equation AXB-C=0 |
|
Song Chuanning, Xu Qingxiang
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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. |
| Key words: Moore-Penrose inverse Frobenius norm 2-norm |
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