| 两类分块矩阵的群逆 |
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| 引用本文： | 张倍欣,冯茂春.两类分块矩阵的群逆[J].湖州师专学报,2011(2):41-45. |
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| 作者姓名： | 张倍欣 冯茂春 |
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| 作者单位： | 湖州师范学院理学院,浙江湖卅I313000 |
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| 基金项目： | 湖州师范学院教改重点项目（2008JY006）. |
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| 摘 要： | 当P为退化的幂等矩阵时,我们利用矩阵的秩的性质、分块矩阵的初等变换,以及群逆存在的充分必要条件,讨论了形如M=P P＋PP＊（P0）和M=P P（P＋PP＊0）（其中P为方阵）的两类分块矩阵群逆的存在性.接着,利用初等变换和矩阵1逆的求法,根据矩阵群逆与矩阵3次幂的1逆的关系,最终给出上述两类分块矩阵群逆的一般表示式,并以例子加以说明
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| 关 键 词： | 分块矩阵 矩阵的群逆 酉矩阵 |
The Group Inverse of Two Classes of Block Matrix |
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| Authors: | ZHANG Bei-xin FENG Mao-chun |
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| Institution: | (School of Science,Huzhou Teachers College,Huzhou 313000,China) |
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| Abstract: | When P is singular idempotent matrix,using the properties of matrixes rank,elementary transformation of block matrix,and necessary and sufficient condition for the existence of group inverse,we discuss the existence of group inverse of block matrix shaped likeM=P P＋PP＊ P 0and M=P P P＋PP＊ 0（P is square matrix）.Next,using elementary transformation and calculation method for 1 inverse of matrix,according to the relation of matrices’ group inverses and 1 inverse of 3 power of matrix.Finally we give the general expression of the two kind of block matrixes’ group inverse,and illustrate it with examples |
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| Keywords: | block matrix group inverse of matrix stepped matrix |
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