| 矩阵之积的(T,S,2)-逆的反序律 |
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| 引用本文： | 陈永林.矩阵之积的(T,S,2)-逆的反序律[J].南京师大学报,2004,27(3):12-16. |
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| 作者姓名： | 陈永林 |
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| 作者单位： | 南京师范大学数学与计算机科学学院 210097江苏，南京 |
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| 摘 要： | 给出了矩阵积的(T，S，2)-逆的反序律成立的充分必要条件．这一结果适用于包括Moofe-Petmse逆、Drazin逆等在内的大多数常用广义逆矩阵．另外，证明了等式(AB)^ MP=(A^ MNAB)^ NP(ABB^ NP)^ MN
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| 关 键 词： | （T，S，2）-广义逆 反序律 矩阵积 |
| 文章编号： | 1001-4616(2004)03-0012-05 |
| 修稿时间： | 2003年9月25日 |
Reverse Order Law for the (T,S,2)-Inverse of a Matrix Product |
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| Chen Yonglin.Reverse Order Law for the (T,S,2)-Inverse of a Matrix Product[J].Journal of Nanjing Normal University(Natural Science Edition),2004,27(3):12-16. |
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| Authors: | Chen Yonglin |
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| Abstract: | The necessary and sufficient condition for the validity of the reverse order law for the (T,S,2)-inverse of a matrix product is given. This result applies to the most of the commonly used generalized inverses of matrices including the Moore-Penrose inverse, the Drazin inverse and the others. In addition, the equality (AB)~+_(MP)=(A~+_(MN)AB)~+_(NP)(ABB~+_(NP))~+_(MN) is proved. |
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| Keywords: | (T S 2)-generalized inverse reverse order law matrix product |
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