| 分块矩阵广义逆的几种表达式 |
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| 引用本文： | 许赟,孙乐平.分块矩阵广义逆的几种表达式[J].上海师范大学学报(自然科学版),2007,36(5):15-21. |
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| 作者姓名： | 许赟 孙乐平 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234 |
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| 摘 要： | 受分块矩阵的逆矩阵形式的启发，给出了分块矩阵A=（A11 A12 A21 A22）的广义逆A^（1，3），A^（2），A^＋，Ad和Ag可以表示为X=（S1^α-A11^αA12S2^α -A11^αA21S1^α S2^α）的条件；然后运用这些结果，得到分块矩阵A的M—P逆的几个表达式；最后给出一个求分块矩阵M—P逆的例子．
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| 关 键 词： | Moore-penrose逆 Drazin逆 分块矩阵 |
| 文章编号： | 1000-5137（2007）05-0015-07 |
| 修稿时间： | 2007-03-20 |
Some expressions of the generalized inverses of a partitioned matrix |
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| XU Yun,SUN Le-ping.Some expressions of the generalized inverses of a partitioned matrix[J].Journal of Shanghai Normal University(Natural Sciences),2007,36(5):15-21. |
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| Authors: | XU Yun SUN Le-ping |
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| Institution: | College of Mathematics and Sciences, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | We show the conditions under which the generalized inverses A(1,3) , A(2) , A+, Ad and Ag of the partitioned matrixA= (A11 A12 A21 A22) can be expressed in the form of X = ( Sα1 -Aα11A12Sα2 -Aα22A21Sα1 Sα2),which is induced,from the form of the inverse of the partitioned matrix A. Then from the results, we derive some other expressions of the Moore - Penrose inverse of the partitioned matrix A. Then from the M-P inverse of its blocks. Finally, we offer an example. |
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| Keywords: | Moore-penrose inverse Drazin inverse partitioned matrix |
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