| 分块矩阵Moore－Penrose广义逆的一个表达式 |
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| 引用本文： | 傅鹂.分块矩阵Moore－Penrose广义逆的一个表达式[J].重庆大学学报(自然科学版),1994(3). |
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| 作者姓名： | 傅鹂 |
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| 作者单位： | 系统工程及应用数学系 |
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| 摘 要： | 给出了按列或按行分块的矩阵Ｍｏｏｒｅ－ｐｅｎｒｏｓｅ广义逆的一个公式及其基于Ｐｅｎｒｏｓｅ方程组的直接证明，对一些重要特例作了推论。证明中给出的有关引理还包含了关于Ｍ一Ｐ逆阵及正交投影阵的若干有用性质。
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| 关 键 词： | 矩阵 广义逆 正交投影 |
An Explicit Formula for the Moore-penrose Generalized Inverse of a Partitioned Matrix |
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| FuLi.An Explicit Formula for the Moore-penrose Generalized Inverse of a Partitioned Matrix[J].Journal of Chongqing University(Natural Science Edition),1994(3). |
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| Authors: | FuLi |
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| Abstract: | An explicit formula was given for the Moore-Penrose generalized inverse of amatrix being partitioned by columns or by rows with its proof directly based on Penrose'S equations. Corollaries were obtained for some important special cases. Several useful properties of M-P inveise of matrix and the orthogonal projection matrix were included in some of the lemmas given in the proof. |
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| Keywords: | matrix generalized inverse orthogonal projection |
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