| 体上带有和与差形式子块的分块矩阵的群逆 |
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| 引用本文： | 卜长江,张奎泽,韩晓光.体上带有和与差形式子块的分块矩阵的群逆[J].黑龙江大学自然科学学报,2009,26(5). |
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| 作者姓名： | 卜长江 张奎泽 韩晓光 |
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| 作者单位： | 哈尔滨工程大学理学院,哈尔滨,150001 |
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| 基金项目： | 黑龙江省自然科学基金资助项目(59110120002) |
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| 摘 要： | 对于体上n阶方阵A,称满足方程AXA=A,XAX=X,AX=XA的n阶方阵X为矩阵A的群逆。分块矩阵的群逆的存在性和表达式的研究不仅有重要的理论意义,而且有广泛的应用价值。分块矩阵(CAB0)的群逆存在性和表达式是一个未解决的问题。主要给出体上分块矩阵(CAB0)(其中A,B群逆存在且C=±(A+B),或者A,B群逆存在且C=±(A-B))的群逆存在的充分必要条件和表达式。
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| 关 键 词： | 体 特征 分块矩阵 群逆 Drazin逆 |
Group inverses of block matrices with a sub-block in the form of sum or difference over skew fields |
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| BU Chang-jiang,ZHANG Kui-ze,HAN Xiao-guang.Group inverses of block matrices with a sub-block in the form of sum or difference over skew fields[J].Journal of Natural Science of Heilongjiang University,2009,26(5). |
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| Authors: | BU Chang-jiang ZHANG Kui-ze HAN Xiao-guang |
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| Institution: | College of Science;Harbin Engineering University;Harbin 150001;China |
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| Abstract: | For an n× n matrix A over a skew field, the n ×n matrix X is called the group inverse of A, if it satisfying the matrix equations AXA = A, XAX = X, AX = XA. Investigating the existence and representation of group inverses for block matrices not only have important theoretical significance but also extensive application value.At pres- ent, the existence and representation of group inverse for block matrix(C A B 0) is still an open problem.Necessary and sufficient conditions for existence and representation of group inverse of the block matrix(C A B 0) over skew fields is given for the cases:(I) A~#,B~# exist and C = ±(A +B) ; and (ii)A~#,B~# exist and C = ± (A -B) ). |
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| Keywords: | skew field character block matrix group inverse Drazin inverse |
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