| 关于2×2块矩阵在除环上群逆的注记 |
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| 引用本文： | 刘新,杨晓英.关于2×2块矩阵在除环上群逆的注记[J].成都信息工程学院学报,2012,27(5):516-519. |
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| 作者姓名： | 刘新 杨晓英 |
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| 作者单位： | 四川信息职业技术学院基础教育部,四川广元,628017 |
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| 摘 要： | 针对分块矩阵在除环上群逆的表示,在证明中使用的引理并不能根据所给条件判定得到分块矩阵群逆的存在性,采用举反例的方法说明存在的问题,进而通过在原有题设中添加了一个条件,证明了分块矩阵的群逆存在,从而更正了定理内容。利用一个新引理和分块矩阵的子矩阵的秩之间的关系证明得到2×2块矩阵在除环上群逆表示的一个新的结果.
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| 关 键 词： | 计算数学 广义逆 群逆 除环 |
A Note on Group Inverse for a Class 2 × 2 Block Matrices over Skew Fields |
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| LIU Xin
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YANG Xiao-ying.A Note on Group Inverse for a Class 2 × 2 Block Matrices over Skew Fields[J].Journal of Chengdu University of Information Technology,2012,27(5):516-519. |
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| Authors: | LIU Xin YANG Xiao-ying |
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| Institution: | (Ministry of Basic Education, Sichnan Information Technology College, Guangyuan 628017, China) |
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| Abstract: | For the lemma which is used for proving group inverse for a class of 2 x 2 block matrices over skew fields, this paper points out that the conditions of the lemma can not determine the existence of block matrix＇ s group in- verse. Then a condition is added in the original title set to prove the existence of group inverse for the block matrix and the content of theorem is corrected. In addition, a new result on group inverse for a class of 2 x 2 block matrices over skew fields is presented by a new lemma and the relationship between the rank of submatrix for the block ma- trix. |
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| Keywords: | computational mathematics generalized inverse group inverse skew fields |
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