| 关于除环上分块矩阵的Marsaglia-Styan秩公式的注记 |
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| 引用本文： | 杨忠鹏,冯晓霞.关于除环上分块矩阵的Marsaglia-Styan秩公式的注记[J].莆田学院学报,2010,17(2):18-22. |
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| 作者姓名： | 杨忠鹏 冯晓霞 |
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| 作者单位： | 1. 莆田学院,数学与应用数学系,福建,莆田,351100
2. 漳州师范学院,数学系,福建,漳州,363000 |
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| 基金项目： | 福建省高校服务海西建设重点项目，福建省教育厅科技项目，莆田学院教学研究项目 |
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| 摘 要： | 指出已有文献中的除环上2×2分块矩阵ABC:D的Marsaglia-Styan秩公式和数域上的表达形式是相同的,即其表达式中三处出现的A的:1:-广义逆都是相同的。应用除环上的初等变换的方法,证明了分块矩阵的Marsaglia-Styan秩公式的表达式中的三处也可以选择不同的A的:1:-广义逆。
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| 关 键 词： | 除环 分块矩阵 Marsaglia-Styan秩公式 :1:-广义逆 初等变换 |
Notes on the Marsaglia-Styan Rank Formula of Partitioning Matrix over a Division Ring |
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| YANG Zhong-peng,FENG Xiao-xia.Notes on the Marsaglia-Styan Rank Formula of Partitioning Matrix over a Division Ring[J].journal of putian university,2010,17(2):18-22. |
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| Authors: | YANG Zhong-peng FENG Xiao-xia |
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| Institution: | 1.Mathematics & Applied Mathematics Department/a>;Putian University/a>;Putian Fujian 351100/a>;China/a>;2.Department of Mathematics/a>;Zhangzhou Normal University/a>;Zhangzhou Fujian 363000/a>;China |
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| Abstract: | In all the available articles,the expression form of Marsaglia-Styan rank formula of 2×2 partitioning matrix A B C:D over division rings is the same as it over number fields,that is,the three:1:-generalized inverses of A appearing in the formula are the same.In this paper,by using the method of elementary transformation of division rings,we prove that the three:1:-generalized inverses of A appearing in the formula of Marsaglia-Styan rank formula on partitioning matrix can be different. |
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| Keywords: | division ring partitioning matrix Marsaglia-Styan rank formula :1:-generalized inverse elementary transformation |
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