| 一类2×2分块矩阵的广义逆 |
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| 引用本文： | 徐海雯,孙乐平,王国荣.一类2×2分块矩阵的广义逆[J].上海师范大学学报(自然科学版),2007,36(3):34-39. |
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| 作者姓名： | 徐海雯 孙乐平 王国荣 |
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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： | 讨论了一类2×2分块矩阵在某些特殊条件下各种各样的广义逆,包括M-P逆,加权M-P逆,群逆,Drazin逆.这些广义逆的表达式都建立在M(2)T,S的基础上,由于它们都是具有相应值域和零空间的{2}逆.
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| 关 键 词： | 可相乘矩阵 分块矩阵 广义逆 满秩分解 |
| 文章编号： | 1000-5137(2007)03-0034-06 |
| 修稿时间： | 2007年3月10日 |
Generalized inverses of a 2×2 block partitioned matrix |
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| XU Hai-wen,SUN Le-ping,WANG Guo-rong.Generalized inverses of a 2×2 block partitioned matrix[J].Journal of Shanghai Normal University(Natural Sciences),2007,36(3):34-39. |
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| Authors: | XU Hai-wen SUN Le-ping WANG Guo-rong |
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| Abstract: | All kinds of generalized inverses including M+,M+XY, Mg and Md of a 2×2 block matrix M = (A B C D)are discussed under some conditions. The representations are all based on M(2)T,S=U(VUM)- 1 V since M+,M+XY,Mg and Md are actually some kinds of { 2 } inverses with corresponding prescribed ranges and null spaces, where U and V are full column rank and full row rank matrices respectively such that R(U) = T, N(V) = S. |
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| Keywords: | conformable matrix partitioned matrix generalized inverse full rank factorization |
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